Wow: I just hit the same error right now!

#4 fixed mine. (Run from 1st distro!)

Here's something that might help you with that ...
https://forums.linuxmint.com/viewtopic.php?t=379134

Ok - To give you some "attempts" on my end I have updated to the latest kernel (5.19). Also of interest I booted to MX and used the GUI "Boot Options" software in attempt to move Mint up in the boot sequence...oddly it shown "success" after the change but when i reboot MX is still first in the boot sequ3ence options.

Here are the results for the above

root@mint-System-Product-Name:/# cat boot/grub/grub.cfg
#
# DO NOT EDIT THIS FILE
#
# It is automatically generated by grub-mkconfig using templates
# from /etc/grub.d and settings from /etc/default/grub
#

### BEGIN /etc/grub.d/00_header ###
if [ -s $prefix/grubenv ]; then
set have_grubenv=true
load_env
fi
if [ "${initrdfail}" = 2 ]; then
set initrdfail=
elif [ "${initrdfail}" = 1 ]; then
set next_entry="${prev_entry}"
set prev_entry=
save_env prev_entry
if [ "${next_entry}" ]; then
set initrdfail=2
fi
fi
if [ "${next_entry}" ] ; then
set default="${next_entry}"
set next_entry=
save_env next_entry
set boot_once=true
else
set default="MX 19.3 patito feo (19.3 ) (on /dev/sda1)"
fi

if [ x"${feature_menuentry_id}" = xy ]; then
menuentry_id_option="--id"
else
menuentry_id_option=""
fi

export menuentry_id_option

if [ "${prev_saved_entry}" ]; then
set saved_entry="${prev_saved_entry}"
save_env saved_entry
set prev_saved_entry=
save_env prev_saved_entry
set boot_once=true
fi

function savedefault {
if [ -z "${boot_once}" ]; then
saved_entry="${chosen}"
save_env saved_entry
fi
}
function initrdfail {
if [ -n "${have_grubenv}" ]; then if [ -n "${partuuid}" ]; then
if [ -z "${initrdfail}" ]; then
set initrdfail=1
if [ -n "${boot_once}" ]; then
set prev_entry="${default}"
save_env prev_entry
fi
fi
save_env initrdfail
fi; fi
}
function recordfail {
set recordfail=1
if [ -n "${have_grubenv}" ]; then if [ -z "${boot_once}" ]; then save_env recordfail; fi; fi
}
function load_video {
if [ x$feature_all_video_module = xy ]; then
insmod all_video
else
insmod efi_gop
insmod efi_uga
insmod ieee1275_fb
insmod vbe
insmod vga
insmod video_bochs
insmod video_cirrus
fi
}

if [ x$feature_default_font_path = xy ] ; then
font=unicode
else
insmod part_msdos
insmod ext2
set root='hd0,msdos5'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd0,msdos5 --hint-efi=hd0,msdos5 --hint-baremetal=ahci0,msdos5 245d8512-eee9-47a3-8dd9-17952920d509
else
search --no-floppy --fs-uuid --set=root 245d8512-eee9-47a3-8dd9-17952920d509
fi
font="/usr/share/grub/unicode.pf2"
fi

if loadfont $font ; then
set gfxmode=auto
load_video
insmod gfxterm
set locale_dir=$prefix/locale
set lang=en_US
insmod gettext
fi
terminal_output gfxterm
if [ "${recordfail}" = 1 ] ; then
set timeout=30
else
if [ x$feature_timeout_style = xy ] ; then
set timeout_style=hidden
set timeout=8
# Fallback hidden-timeout code in case the timeout_style feature is
# unavailable.
elif sleep --interruptible 8 ; then
set timeout=0
fi
fi
### END /etc/grub.d/00_header ###

### BEGIN /etc/grub.d/05_debian_theme ###
set menu_color_normal=white/black
set menu_color_highlight=black/light-gray
### END /etc/grub.d/05_debian_theme ###

### BEGIN /etc/grub.d/10_linux_proxy ###

function gfxmode {
set gfxpayload="${1}"
if [ "${1}" = "keep" ]; then
set vt_handoff=vt.handoff=7
else
set vt_handoff=
fi
}
if [ "${recordfail}" != 1 ]; then
if [ -e ${prefix}/gfxblacklist.txt ]; then
if [ ${grub_platform} != pc ]; then
set linux_gfx_mode=keep
elif hwmatch ${prefix}/gfxblacklist.txt 3; then
if [ ${match} = 0 ]; then
set linux_gfx_mode=keep
else
set linux_gfx_mode=text
fi
else
set linux_gfx_mode=text
fi
else
set linux_gfx_mode=keep
fi
else
set linux_gfx_mode=text
fi
export linux_gfx_mode



### END /etc/grub.d/10_linux_proxy ###

### BEGIN /etc/grub.d/30_os-prober_proxy ###
menuentry "MX Linux 19.4 patito feo (19.4 ) (on /dev/sda1)" --class mx --class gnu-linux --class gnu --class os $menuentry_id_option 'osprober-gnulinux-simple-6e5181d4-1b59-40ff-8133-495a43ecbbd5' {
insmod part_msdos
insmod ext2
set root='hd0,msdos1'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd0,msdos1 --hint-efi=hd0,msdos1 --hint-baremetal=ahci0,msdos1 6e5181d4-1b59-40ff-8133-495a43ecbbd5
else
search --no-floppy --fs-uuid --set=root 6e5181d4-1b59-40ff-8133-495a43ecbbd5
fi
linux /boot/vmlinuz-4.19.0-14-amd64 root=UUID=6e5181d4-1b59-40ff-8133-495a43ecbbd5 ro quiet splash
initrd /boot/initrd.img-4.19.0-14-amd64
}
### END /etc/grub.d/30_os-prober_proxy ###

### BEGIN /etc/grub.d/40_custom_proxy ###
menuentry "Linux Mint" --class ubuntu --class gnu-linux --class gnu --class os $menuentry_id_option 'gnulinux-simple-245d8512-eee9-47a3-8dd9-17952920d509' {
recordfail
load_video
gfxmode $linux_gfx_mode
insmod gzio
if [ x$grub_platform = xxen ]; then insmod xzio; insmod lzopio; fi
insmod part_msdos
insmod ext2
set root='hd0,msdos5'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd0,msdos5 --hint-efi=hd0,msdos5 --hint-baremetal=ahci0,msdos5 245d8512-eee9-47a3-8dd9-17952920d509
else
search --no-floppy --fs-uuid --set=root 245d8512-eee9-47a3-8dd9-17952920d509
fi
linux /boot/vmlinuz-5.4.0-146-generic root=UUID=245d8512-eee9-47a3-8dd9-17952920d509 ro quiet splash $vt_handoff
initrd /boot/initrd.img-5.4.0-146-generic
}
### END /etc/grub.d/40_custom_proxy ###

### BEGIN /etc/grub.d/41_linux_proxy ###
submenu "Advanced options for Ubuntu"{
menuentry "Ubuntu, with Linux 5.19.0-41-generic" --class ubuntu --class gnu-linux --class gnu --class os $menuentry_id_option 'gnulinux-5.19.0-41-generic-advanced-245d8512-eee9-47a3-8dd9-17952920d509' {
recordfail
load_video
gfxmode $linux_gfx_mode
insmod gzio
if [ x$grub_platform = xxen ]; then insmod xzio; insmod lzopio; fi
insmod part_msdos
insmod ext2
set root='hd0,msdos5'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd0,msdos5 --hint-efi=hd0,msdos5 --hint-baremetal=ahci0,msdos5 245d8512-eee9-47a3-8dd9-17952920d509
else
search --no-floppy --fs-uuid --set=root 245d8512-eee9-47a3-8dd9-17952920d509
fi
echo 'Loading Linux 5.19.0-41-generic ...'
linux /boot/vmlinuz-5.19.0-41-generic root=UUID=245d8512-eee9-47a3-8dd9-17952920d509 ro quiet splash $vt_handoff
echo 'Loading initial ramdisk ...'
initrd /boot/initrd.img-5.19.0-41-generic
}
menuentry "Ubuntu, with Linux 5.19.0-41-generic (recovery mode)" --class ubuntu --class gnu-linux --class gnu --class os $menuentry_id_option 'gnulinux-5.19.0-41-generic-recovery-245d8512-eee9-47a3-8dd9-17952920d509' {
recordfail
load_video
insmod gzio
if [ x$grub_platform = xxen ]; then insmod xzio; insmod lzopio; fi
insmod part_msdos
insmod ext2
set root='hd0,msdos5'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd0,msdos5 --hint-efi=hd0,msdos5 --hint-baremetal=ahci0,msdos5 245d8512-eee9-47a3-8dd9-17952920d509
else
search --no-floppy --fs-uuid --set=root 245d8512-eee9-47a3-8dd9-17952920d509
fi
echo 'Loading Linux 5.19.0-41-generic ...'
linux /boot/vmlinuz-5.19.0-41-generic root=UUID=245d8512-eee9-47a3-8dd9-17952920d509 ro recovery nomodeset dis_ucode_ldr
echo 'Loading initial ramdisk ...'
initrd /boot/initrd.img-5.19.0-41-generic
}
menuentry "Ubuntu, with Linux 5.15.0-71-generic" --class ubuntu --class gnu-linux --class gnu --class os $menuentry_id_option 'gnulinux-5.15.0-71-generic-advanced-245d8512-eee9-47a3-8dd9-17952920d509' {
recordfail
load_video
gfxmode $linux_gfx_mode
insmod gzio
if [ x$grub_platform = xxen ]; then insmod xzio; insmod lzopio; fi
insmod part_msdos
insmod ext2
set root='hd0,msdos5'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd0,msdos5 --hint-efi=hd0,msdos5 --hint-baremetal=ahci0,msdos5 245d8512-eee9-47a3-8dd9-17952920d509
else
search --no-floppy --fs-uuid --set=root 245d8512-eee9-47a3-8dd9-17952920d509
fi
echo 'Loading Linux 5.15.0-71-generic ...'
linux /boot/vmlinuz-5.15.0-71-generic root=UUID=245d8512-eee9-47a3-8dd9-17952920d509 ro quiet splash $vt_handoff
echo 'Loading initial ramdisk ...'
initrd /boot/initrd.img-5.15.0-71-generic
}
menuentry "Ubuntu, with Linux 5.15.0-71-generic (recovery mode)" --class ubuntu --class gnu-linux --class gnu --class os $menuentry_id_option 'gnulinux-5.15.0-71-generic-recovery-245d8512-eee9-47a3-8dd9-17952920d509' {
recordfail
load_video
insmod gzio
if [ x$grub_platform = xxen ]; then insmod xzio; insmod lzopio; fi
insmod part_msdos
insmod ext2
set root='hd0,msdos5'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd0,msdos5 --hint-efi=hd0,msdos5 --hint-baremetal=ahci0,msdos5 245d8512-eee9-47a3-8dd9-17952920d509
else
search --no-floppy --fs-uuid --set=root 245d8512-eee9-47a3-8dd9-17952920d509
fi
echo 'Loading Linux 5.15.0-71-generic ...'
linux /boot/vmlinuz-5.15.0-71-generic root=UUID=245d8512-eee9-47a3-8dd9-17952920d509 ro recovery nomodeset dis_ucode_ldr
echo 'Loading initial ramdisk ...'
initrd /boot/initrd.img-5.15.0-71-generic
}
}
### END /etc/grub.d/41_linux_proxy ###

### BEGIN /etc/grub.d/42_linux_zfs ###
### END /etc/grub.d/42_linux_zfs ###

### BEGIN /etc/grub.d/43_linux_xen ###

### END /etc/grub.d/43_linux_xen ###

### BEGIN /etc/grub.d/44_os-prober_proxy ###
menuentry "Microsoft Windows XP Professional (on /dev/sdf1)" --class windows --class os $menuentry_id_option 'osprober-chain-1470355270353BB4' {
insmod part_msdos
insmod ntfs
set root='hd5,msdos1'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd5,msdos1 --hint-efi=hd5,msdos1 --hint-baremetal=ahci5,msdos1 1470355270353BB4
else
search --no-floppy --fs-uuid --set=root 1470355270353BB4
fi
parttool ${root} hidden-
drivemap -s (hd0) ${root}
chainloader +1
}





set timeout_style=menu
if [ "${timeout}" = 0 ]; then
set timeout=10
fi
submenu "Advanced options for MX 19.4 patito feo (19.4 ) (on /dev/sda1)"{
menuentry "Debian GNU/Linux (on /dev/sda1)" --class gnu-linux --class gnu --class os $menuentry_id_option 'osprober-gnulinux-/boot/vmlinuz-4.19.0-14-amd64--6e5181d4-1b59-40ff-8133-495a43ecbbd5' {
insmod part_msdos
insmod ext2
set root='hd0,msdos1'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd0,msdos1 --hint-efi=hd0,msdos1 --hint-baremetal=ahci0,msdos1 6e5181d4-1b59-40ff-8133-495a43ecbbd5
else
search --no-floppy --fs-uuid --set=root 6e5181d4-1b59-40ff-8133-495a43ecbbd5
fi
linux /boot/vmlinuz-4.19.0-14-amd64 root=UUID=6e5181d4-1b59-40ff-8133-495a43ecbbd5 ro quiet splash
initrd /boot/initrd.img-4.19.0-14-amd64
}
menuentry "Debian GNU/Linux, with Linux 4.19.0-14-amd64 (on /dev/sda1)" --class gnu-linux --class gnu --class os $menuentry_id_option 'osprober-gnulinux-/boot/vmlinuz-4.19.0-14-amd64--6e5181d4-1b59-40ff-8133-495a43ecbbd5' {
insmod part_msdos
insmod ext2
set root='hd0,msdos1'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd0,msdos1 --hint-efi=hd0,msdos1 --hint-baremetal=ahci0,msdos1 6e5181d4-1b59-40ff-8133-495a43ecbbd5
else
search --no-floppy --fs-uuid --set=root 6e5181d4-1b59-40ff-8133-495a43ecbbd5
fi
linux /boot/vmlinuz-4.19.0-14-amd64 root=UUID=6e5181d4-1b59-40ff-8133-495a43ecbbd5 ro quiet splash
initrd /boot/initrd.img-4.19.0-14-amd64
}
menuentry "Debian GNU/Linux, with Linux 4.19.0-14-amd64 (systemd) (on /dev/sda1)" --class gnu-linux --class gnu --class os $menuentry_id_option 'osprober-gnulinux-/boot/vmlinuz-4.19.0-14-amd64--6e5181d4-1b59-40ff-8133-495a43ecbbd5' {
insmod part_msdos
insmod ext2
set root='hd0,msdos1'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd0,msdos1 --hint-efi=hd0,msdos1 --hint-baremetal=ahci0,msdos1 6e5181d4-1b59-40ff-8133-495a43ecbbd5
else
search --no-floppy --fs-uuid --set=root 6e5181d4-1b59-40ff-8133-495a43ecbbd5
fi
linux /boot/vmlinuz-4.19.0-14-amd64 root=UUID=6e5181d4-1b59-40ff-8133-495a43ecbbd5 ro quiet splash init=/lib/systemd/systemd
initrd /boot/initrd.img-4.19.0-14-amd64
}
menuentry "Debian GNU/Linux, with Linux 4.19.0-14-amd64 (recovery mode) (on /dev/sda1)" --class gnu-linux --class gnu --class os $menuentry_id_option 'osprober-gnulinux-/boot/vmlinuz-4.19.0-14-amd64-root=UUID=6e5181d4-1b59-40ff-8133-495a43ecbbd5 ro single-6e5181d4-1b59-40ff-8133-495a43ecbbd5' {
insmod part_msdos
insmod ext2
set root='hd0,msdos1'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd0,msdos1 --hint-efi=hd0,msdos1 --hint-baremetal=ahci0,msdos1 6e5181d4-1b59-40ff-8133-495a43ecbbd5
else
search --no-floppy --fs-uuid --set=root 6e5181d4-1b59-40ff-8133-495a43ecbbd5
fi
linux /boot/vmlinuz-4.19.0-14-amd64 root=UUID=6e5181d4-1b59-40ff-8133-495a43ecbbd5 ro single
initrd /boot/initrd.img-4.19.0-14-amd64
}
}
### END /etc/grub.d/44_os-prober_proxy ###

### BEGIN /etc/grub.d/45_uefi-firmware ###
### END /etc/grub.d/45_uefi-firmware ###

### BEGIN /etc/grub.d/46_fwupd ###
### END /etc/grub.d/46_fwupd ###

### BEGIN /etc/grub.d/47_custom_proxy ###

# This file provides an easy way to add custom menu entries. Simply type the
# menu entries you want to add after this comment. Be careful not to change
# the 'exec tail' line above.

### END /etc/grub.d/47_custom_proxy ###

### BEGIN /etc/grub.d/48_custom ###
if [ -f ${config_directory}/custom.cfg ]; then
source ${config_directory}/custom.cfg
elif [ -z "${config_directory}" -a -f $prefix/custom.cfg ]; then
source $prefix/custom.cfg;
fi
### END /etc/grub.d/48_custom ###
root@mint-System-Product-Name:/#


root@mint-System-Product-Name:/etc# ls -R /etc/grub.d
/etc/grub.d:
00_header 30_uefi-firmware.dpkg-dist 46_fwupd
05_debian_theme 40_custom_proxy 47_custom_proxy
10_linux.dpkg-dist 41_custom.dpkg-dist 48_custom
10_linux_proxy 41_linux_proxy backup
10_linux_zfs.dpkg-dist 42_linux_zfs bin
20_linux_xen.dpkg-dist 43_linux_xen proxifiedScripts
30_os-prober.dpkg-dist 44_os-prober_proxy README
30_os-prober_proxy 45_uefi-firmware

/etc/grub.d/backup:
boot_grub default_grub etc_grub_d RESTORE_INSTRUCTIONS

/etc/grub.d/backup/boot_grub:
fonts gfxblacklist.txt grub.cfg grubenv i386-pc unicode.pf2

/etc/grub.d/backup/boot_grub/fonts:
unicode.pf2

/etc/grub.d/backup/boot_grub/i386-pc:
915resolution.mod gcry_twofish.mod pbkdf2.mod
acpi.mod gcry_whirlpool.mod pbkdf2_test.mod
adler32.mod gdb.mod pcidump.mod
affs.mod geli.mod pci.mod
afs.mod gettext.mod pgp.mod
ahci.mod gfxmenu.mod plan9.mod
all_video.mod gfxterm_background.mod play.mod
aout.mod gfxterm_menu.mod png.mod
archelp.mod gfxterm.mod priority_queue.mod
ata.mod gptsync.mod probe.mod
at_keyboard.mod gzio.mod procfs.mod
backtrace.mod halt.mod progress.mod
bfs.mod hashsum.mod pxechain.mod
biosdisk.mod hdparm.mod pxe.mod
bitmap.mod hello.mod raid5rec.mod
bitmap_scale.mod help.mod raid6rec.mod
blocklist.mod hexdump.mod random.mod
boot.img hfs.mod rdmsr.mod
boot.mod hfspluscomp.mod read.mod
bsd.mod hfsplus.mod reboot.mod
bswap_test.mod http.mod regexp.mod
btrfs.mod hwmatch.mod reiserfs.mod
bufio.mod iorw.mod relocator.mod
cat.mod iso9660.mod romfs.mod
cbfs.mod jfs.mod scsi.mod
cbls.mod jpeg.mod search_fs_file.mod
cbmemc.mod keylayouts.mod search_fs_uuid.mod
cbtable.mod keystatus.mod search_label.mod
cbtime.mod ldm.mod search.mod
chain.mod legacycfg.mod sendkey.mod
cmdline_cat_test.mod legacy_password_test.mod serial.mod
cmosdump.mod linux16.mod setjmp.mod
cmostest.mod linux.mod setjmp_test.mod
cmp.mod loadenv.mod setpci.mod
cmp_test.mod loopback.mod sfs.mod
command.lst lsacpi.mod shift_test.mod
configfile.mod lsapm.mod signature_test.mod
core.img lsmmap.mod sleep.mod
cpio_be.mod ls.mod sleep_test.mod
cpio.mod lspci.mod smbios.mod
cpuid.mod luks.mod spkmodem.mod
crc64.mod lvm.mod squash4.mod
cryptodisk.mod lzopio.mod strtoull_test.mod
crypto.lst macbless.mod syslinuxcfg.mod
crypto.mod macho.mod tar.mod
cs5536.mod mda_text.mod terminal.lst
ctz_test.mod mdraid09_be.mod terminal.mod
datehook.mod mdraid09.mod terminfo.mod
date.mod mdraid1x.mod test_blockarg.mod
datetime.mod memdisk.mod testload.mod
diskfilter.mod memrw.mod test.mod
disk.mod minicmd.mod testspeed.mod
div.mod minix2_be.mod tftp.mod
div_test.mod minix2.mod tga.mod
dm_nv.mod minix3_be.mod time.mod
drivemap.mod minix3.mod trig.mod
echo.mod minix_be.mod tr.mod
efiemu32.o minix.mod truecrypt.mod
efiemu64.o mmap.mod true.mod
efiemu.mod moddep.lst udf.mod
ehci.mod modinfo.sh ufs1_be.mod
elf.mod morse.mod ufs1.mod
eval.mod mpi.mod ufs2.mod
exfat.mod msdospart.mod uhci.mod
exfctest.mod mul_test.mod usb_keyboard.mod
ext2.mod multiboot2.mod usb.mod
extcmd.mod multiboot.mod usbms.mod
f2fs.mod nativedisk.mod usbserial_common.mod
fat.mod net.mod usbserial_ftdi.mod
file.mod newc.mod usbserial_pl2303.mod
font.mod nilfs2.mod usbserial_usbdebug.mod
freedos.mod normal.mod usbtest.mod
fshelp.mod ntfscomp.mod vbe.mod
fs.lst ntfs.mod verifiers.mod
functional_test.mod ntldr.mod vga.mod
gcry_arcfour.mod odc.mod vga_text.mod
gcry_blowfish.mod offsetio.mod video_bochs.mod
gcry_camellia.mod ohci.mod video_cirrus.mod
gcry_cast5.mod part_acorn.mod video_colors.mod
gcry_crc.mod part_amiga.mod video_fb.mod
gcry_des.mod part_apple.mod videoinfo.mod
gcry_dsa.mod part_bsd.mod video.lst
gcry_idea.mod part_dfly.mod video.mod
gcry_md4.mod part_dvh.mod videotest_checksum.mod
gcry_md5.mod part_gpt.mod videotest.mod
gcry_rfc2268.mod partmap.lst wrmsr.mod
gcry_rijndael.mod part_msdos.mod xfs.mod
gcry_rmd160.mod part_plan.mod xnu.mod
gcry_rsa.mod part_sun.mod xnu_uuid.mod
gcry_seed.mod part_sunpc.mod xnu_uuid_test.mod
gcry_serpent.mod parttool.lst xzio.mod
gcry_sha1.mod parttool.mod zfscrypt.mod
gcry_sha256.mod password.mod zfsinfo.mod
gcry_sha512.mod password_pbkdf2.mod zfs.mod
gcry_tiger.mod pata.mod zstd.mod

/etc/grub.d/backup/etc_grub_d:
00_header 10_linux 20_linux_xen 30_uefi-firmware 41_custom
05_debian_theme 10_linux_zfs 30_os-prober 40_custom README

/etc/grub.d/bin:
grubcfg_proxy

/etc/grub.d/proxifiedScripts:
custom linux os-prober
root@mint-System-Product-Name:/etc#

Hmmm...Well... i just downloaded and installed the file in your link and it came back with same version was already installed...rebooting now to see if it had any effect!

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boot into linux mint open a terminal
move 40_custom_proxy numerically up in grub.d
Edit 15_custom_proxy to change the linux and initrd line to vmlinuz and initrd.img similar to what you was doing at the grub prompt
next run reboot and see what happens.

Not sure if i was doing this correctly....

mint@mint-System-Product-Name:~$ sudo cp /etc/grub.d/40_custom_proxy /etc/grub.d/15_custom_proxy
[sudo] password for mint:
mint@mint-System-Product-Name:~$ sudo nano /etc/grub.d/15_custom_proxy (see photo i saw nothing to change?)
mint@mint-System-Product-Name:~$
"sudo nano /etc/grub.d/15_custom_proxy"
This brought me to screen in photo but...i couldnt see how to "Edit 15...." you mention

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Maybe it did it...? (I see a 15 but still a 40?)
root@mint-System-Product-Name:/etc/grub.d# ls
00_header 30_os-prober_proxy 45_uefi-firmware
05_debian_theme 30_uefi-firmware.dpkg-dist 46_fwupd
10_linux.dpkg-dist 40_custom_proxy 47_custom_proxy
10_linux_proxy 41_custom.dpkg-dist 48_custom
10_linux_zfs.dpkg-dist 41_linux_proxy backup
15_custom_proxy 42_linux_zfs bin
20_linux_xen.dpkg-dist 43_linux_xen proxifiedScripts
30_os-prober.dpkg-dist 44_os-prober_proxy README
root@mint-System-Product-Name:/etc/grub.d#

root@mint-System-Product-Name:/etc/grub.d# sudo update-grub
Sourcing file `/etc/default/grub'
Sourcing file `/etc/default/grub.d/50_linuxmint.cfg'
Sourcing file `/etc/default/grub.d/init-select.cfg'
Generating grub configuration file ...
Found linux image: /boot/vmlinuz-5.19.0-41-generic
Found initrd image: /boot/initrd.img-5.19.0-41-generic
Found linux image: /boot/vmlinuz-5.15.0-71-generic
Found initrd image: /boot/initrd.img-5.15.0-71-generic
Found MX 19.4 patito feo (19.4 ) on /dev/sda1
Found Microsoft Windows XP Professional on /dev/sdf1
Found linux image: /boot/vmlinuz-5.19.0-41-generic
Found initrd image: /boot/initrd.img-5.19.0-41-generic
Found linux image: /boot/vmlinuz-5.15.0-71-generic
Found initrd image: /boot/initrd.img-5.15.0-71-generic
Found MX 19.4 patito feo (19.4 ) on /dev/sda1
Found Microsoft Windows XP Professional on /dev/sdf1
done
root@mint-System-Product-Name:/etc/grub.d#

Rebooting now...

Post the output of

and

Error still occurs but now there are two boot options for Mint

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This outputs a tremendous amount of garble...let me know if want me to post it.

What about the 40_custom?

root@mint-System-Product-Name:/home/mint# cat /etc/grub.d/backup/etc_grub_d/40_custom
#!/bin/sh
exec tail -n +3 $0
# This file provides an easy way to add custom menu entries. Simply type the
# menu entries you want to add after this comment. Be careful not to change
# the 'exec tail' line above.
root@mint-System-Product-Name:/home/mint#

add this to what is already in 15_custom:

reboot

root@mint-System-Product-Name:/etc/grub.d# menuentry "Linux Mint" --class ubuntu --class gnu-linux --class gnu --class os $menuentry_id_option 'gnulinux-simple-245d8512-eee9-47a3-8dd9-17952920d509' {
recordfail
load_video
gfxmode $linux_gfx_mode
insmod gzio
if [ x$grub_platform = xxen ]; then insmod xzio; insmod lzopio; fi
insmod part_msdos
insmod ext2
set root='hd0,msdos5'
if [ x$feature_platform_search_hint = xy ]; then
search --no-floppy --fs-uuid --set=root --hint-bios=hd0,msdos5 --hint-efi=hd0,msdos5 --hint-baremetal=ahci0,msdos5 245d8512-eee9-47a3-8dd9-17952920d509
else
search --no-floppy --fs-uuid --set=root 245d8512-eee9-47a3-8dd9-17952920d509
fi
linux /boot/vmlinuz root=UUID=245d8512-eee9-47a3-8dd9-17952920d509 ro quiet splash $vt_handoff
initrd /boot/initrd.img
}
menuentry: command not found
recordfail: command not found
load_video: command not found
gfxmode: command not found
insmod: ERROR: could not load module gzio: No such file or directory
insmod: ERROR: could not load module part_msdos: No such file or directory
insmod: ERROR: could not load module ext2: No such file or directory
usage: search [arguments] [options]
arguments:
for text
in directory
options:
-c | --case-sensitive
-s | --show-filenames-only
linux: command not found
initrd: command not found
bash: syntax error near unexpected token `}'
root@mint-System-Product-Name:/etc/grub.d#

root@mint-System-Product-Name:/etc/grub.d# sudo update-grub
Sourcing file `/etc/default/grub'
Sourcing file `/etc/default/grub.d/50_linuxmint.cfg'
Sourcing file `/etc/default/grub.d/init-select.cfg'
Generating grub configuration file ...
Found linux image: /boot/vmlinuz-5.19.0-41-generic
Found initrd image: /boot/initrd.img-5.19.0-41-generic
Found linux image: /boot/vmlinuz-5.15.0-71-generic
Found initrd image: /boot/initrd.img-5.15.0-71-generic
Found MX 19.4 patito feo (19.4 ) on /dev/sda1
Found Microsoft Windows XP Professional on /dev/sdf1
Found linux image: /boot/vmlinuz-5.19.0-41-generic
Found initrd image: /boot/initrd.img-5.19.0-41-generic
Found linux image: /boot/vmlinuz-5.15.0-71-generic
Found initrd image: /boot/initrd.img-5.15.0-71-generic
Found MX 19.4 patito feo (19.4 ) on /dev/sda1
Found Microsoft Windows XP Professional on /dev/sdf1
done
root@mint-System-Product-Name:/etc/grub.d#

change it to this: