Since I couldn't find a solution within a week, I now reinstalled the OS. Therefore, I would now consider this thread closed.

------

The Problem:
If I try to boot the OS I get a "corrupted page table" error, even though I can access my system/files just fine using the GUI rescue mode of the Debian online Installer (the original medium I used to install the OS).
edit: even though I don't think I changed anything, I now instead get a different Error: "Volume group "[groupname]" not found"
"Cannot process volume group [groupname]". I'm not sure if that's better or worse.

How it happened:
I tried to upgrade from stable to testing. During the upgrade process I somehow managed to accidentally remove many packages, which rendered me unable to connect to the internet.
First I tried to somehow reinstall the packages despite not having internet, which is apparently possible, but I couldn't figure it out. At this point at least booting my system was still possible.
Then I gave up, made a backup of my home folder and proceeded to boot the Debian Installer in order to reinstall the OS. But there I found the "rescue mode" and tried it. Sure enough was able to get an internet connection and an "interactive shell" on my system. I used this shell to reinstall (hopefully) everything I deleted. I used the standard apt commands to do this.
But after this I now get the "corrupted page table" error at boot (after grub).

More info:
Could I just reinstall the OS: Yes, but I'm rather new to GNU/Linux and would like to learn to how actually to fix stuff (or preferably not break it in the first place).
My system is installed on a single 2TB HDD with only 500GB allocated, because for some reason the installer recommended it. I chose to use the ext4 format and the LVM with the standard fulldisk encryption, iirc truecrypt.
The installer rescue mode gave me different options on where to open the shell, I always used the preselected /dev/debianPC-vg/root option.
Using lsblk in the installer rescue shell I can see 3 partitions on my drive:
sdc1 (487M, part, mounted in /boot)
sdc2 (1K, part, not mounted)
sdc5(1.8T, part, not mounted)
..|-sdc5_crypt (1.8T, crypt, not mounted)
.....|-debianPC--vg-root (464.7G, lvm, mounted in /)
.....|-debainPC--bg-swap_1 (976M, lvm, not mounted)
Using blkid in in the initramfs shell I get dropped into after failing normal boot, I only get 2 partitions (this is after getting the new error, I didn't try before):
/dev/sdb1 type=ext2, blocksize=1024, UUID, PARTUUID
/dev/sdb5 type=crypto_LUKS, UUID, PARTUUID
Back in the installer shell, I used the analyze function of testdisk on /dev/sdc, which finds all 3 partitions and displays "Structure: Ok" for all of them. Testdisk labels them as "ext2", "Linux_LUKS" and "CramFS".

Any help will be greatly appreciated.

"Corrupted page table" refers to memory. The first thing I'd do is to ensure all RAM modules are properly connected and then to check RAM with memtest.

I'm pretty sure that this issue is only related to the data on my HDD and neither to hardware nor to mainboard firmware. I also have Windows installed on a separate drive, which runs perfectly fine. I also tried booting a Lubuntu live USB stick, which runs fine. I'm currently running a memtest86 test, but I doubt it'll find anything.
Thanks for the answer anyway, seems like the original error message doesn't make much sense then? I thought it would refer to a partition table.
Any ideas about the new error?

The page table error is the kernel telling you some-thing is screwing with kernel-space. Given the rescue mode worked I'd be pointing the finger at a video driver. You using nvidea or Radeon video card with proprietary driver ?.
If your re-installs got rid of the message, just forget about it and save the angst.

It would appear LVM hasn't been installed - or at least hasn't been configured properly. The package may be called LVM2 (I don't use Debian so can't check). LVM is block level device emulator that supports flexible allocation of devices and movement of space between them. It's what exposes debianPC--vg-root and debainPC--bg-swap_1.
LVM also need to be built into the initrd - without more context I can't say whether the initrd or kernel is issuing that volume group message. I'd suspect the former.

memtest86 completed without errors


I didn't install any more packages after the initial page table error, I just rebooted a few times switching between rescue mode and the initramfs shell and then suddenly got the new error.
Installing packages with rescue mode is what caused the first error!

I use the nvidia proprietary driver.
My System: AMD Ryzen 3600, Nvidia GTX 1060, G.Skill 2x 8GB 3200MHz

lvm2 was already installed.
In rescue mode I tried:
vgchange -ay /dev/debianPC-vg
>2 logical volume(s) in volume group "debianPC-vg" now active
But that didn't help.
In rescue mode all outputs from lvm like pvdisplay, vgdisplay, lvdisplay make sense.
In the initramfs shell none of these commands return anything.
I compared the output of lvm version and lvm config in both shells. The only difference is that lvm version returns driver version 4.39.0 in rescue mode and 4.43.0 in the initramfs shell.
Here is the output of both commands in rescue mode:

lvm version
LVM version: 2.03.11(2) (2021-01-08)
Library version: 1.02.175 (2021-01-08)
Driver version: 4.39.0
Configuration: ./configure --build=x86_64-linux-gnu --prefix=/usr --includedir=${prefix}/include --mandir=${prefix}/share/man --infodir=${prefix}/share/info --sysconfdir=/etc --localstatedir=/var --disable-option-checking --disable-silent-rules --libdir=${prefix}/lib/x86_64-linux-gnu --runstatedir=/run --disable-maintainer-mode --disable-dependency-tracking --libdir=/lib/x86_64-linux-gnu --sbindir=/sbin --with-usrlibdir=/usr/lib/x86_64-linux-gnu --with-optimisation=-O2 --with-cache=internal --with-device-uid=0 --with-device-gid=6 --with-device-mode=0660 --with-default-pid-dir=/run --with-default-run-dir=/run/lvm --with-default-locking-dir=/run/lock/lvm --with-thin=internal --with-thin-check=/usr/sbin/thin_check --with-thin-dump=/usr/sbin/thin_dump --with-thin-repair=/usr/sbin/thin_repair --with-udev-prefix=/ --enable-applib --enable-blkid_wiping --enable-cmdlib --enable-dmeventd --enable-editline --enable-lvmlockd-dlm --enable-lvmlockd-sanlock --enable-lvmpolld --enable-notify-dbus --enable-pkgconfig --enable-udev_rules --enable-udev_sync --disable-readline

lvm config
config {
checks=1
abort_on_errors=0
profile_dir="/etc/lvm/profile"
}
local {
}
dmeventd {
}
activation {
checks=0
udev_sync=1
udev_rules=1
retry_deactivation=1
missing_stripe_filler="error"
raid_region_size=2048
raid_fault_policy="warn"
mirror_image_fault_policy="remove"
mirror_log_fault_policy="allocate"
snapshot_autoextend_threshold=100
snapshot_autoextend_percent=20
thin_pool_autoextend_threshold=100
thin_pool_autoextend_percent=20
monitoring=1
activation_mode="degraded"
}
global {
umask=63
test=0
units="r"
si_unit_consistency=1
suffix=1
activation=1
proc="/proc"
etc="/etc"
wait_for_locks=1
locking_dir="/run/lock/lvm"
prioritise_write_locks=1
abort_on_internal_errors=0
metadata_read_only=0
mirror_segtype_default="raid1"
raid10_segtype_default="raid10"
sparse_segtype_default="thin"
use_lvmlockd=0
system_id_source="none"
use_lvmpolld=1
notify_dbus=1
}
shell {
history_size=100
}
backup {
backup=1
backup_dir="/etc/lvm/backup"
archive=1
archive_dir="/etc/lvm/archive"
retain_min=10
retain_days=30
}
log {
verbose=0
silent=0
syslog=1
overwrite=0
level=0
command_names=0
prefix=" "
activation=0
debug_classes=["memory","devices","io","activation","allocation","metadata","cache","locking","lvmpolld","dbus"]
}
allocation {
maximise_cling=1
use_blkid_wiping=1
wipe_signatures_when_zeroing_new_lvs=1
mirror_logs_require_separate_pvs=0
}
devices {
dir="/dev"
scan="/dev"
obtain_device_list_from_udev=1
external_device_info_source="none"
sysfs_scan=1
scan_lvs=0
multipath_component_detection=1
md_component_detection=1
fw_raid_component_detection=0
md_chunk_alignment=1
data_alignment_detection=1
data_alignment=0
data_alignment_offset_detection=1
ignore_suspended_devices=0
ignore_lvm_mirrors=1
require_restorefile_with_uuid=1
pv_min_size=2048
issue_discards=0
allow_changes_with_duplicate_pvs=0
allow_mixed_block_sizes=0
}
How do I do this?

--------
Even more info:

The complete output if I boot my system:
--
[ 0.320659] __common_interrupt: 1.55 No irq handler for vector
#[the same for 2.55 to 9.55], this is normal, I always got that
[ 0.320659] __common_interrupt: 10.55 No irq handler for vector
Volume group "debainPC-vg" not found
Cannot process volume group debianPC-vg
#repeat the last two lines a few times
Gave up waiting for suspended/resume device
Volume group "debainPC-vg" not found
Cannot process volume group debianPC-vg
Gave up waiting for root file system device. Common problems:
- Boot args (cat /proc/cmdline)
..- Check rootdelay= (did the system wait long enough?) #yes, yes it did
- Missing modules (cat /proc/modules; ls /dev) #I'll list this below
ALERT! /dev/mapper/debianPC--vg-rot does not exist. Dropping to a shell!

BusyBox v1.30.1 (Debian 1:1.30.1-6+b1) built-in shell (ash)
Enter 'help' for a list of built-in commands.

(initramfs)
--

the first column of "cat /proc/modules":
--
dm_mod
hid_holtek_kbd
sr_mod
sd_mod
cdrom
t10_pi
crc_t10dif
crct10dif_generic
hid_generic
usbhid
hid
crct10dif_pclmul
crct10dif_common
crc32_pclmul
crc32c_intel
ghash_clmulni_intel
ahci
xhci_pci
libahci
xhci_hcd
libata
aesni_intel
r8169
usbcore
libaes
crypto_simd
scsi_mod
realtek
cryptd
mdio_devres
glue_helper
libphy
i2c_piix4
usb_common
wmi
gpio_amdpt
gpio_generic
button
--

ls /dev
--
block
bsg
bus
char
console
cpu_dma_latency
disk
full
gpiochip0
gpiochip1
hidraw0 #1-5 also here
hpet
input
kmsg
#mapper is not here!
mem
null
port
psaux
ptmx
pts
random
rtc
rtc0
#sda-sdc + correct partitions is here
sr0
tty
#tty0 to tty63 is here
#ttyS0 to ttyS3 is here
urandom
usb
vcs
vcs1
vcsa
vcsa1
vcsu
vcsu1
vga_arbiter
zero
--