I have a Dell Inspiron 11 3162, whose primary storage is an eMMC, and recently I was messing around with the mmc-utils package. I mainly downloaded it to check the health of my eMMC, since eMMCs, like all types of flash storage, have a write limit. However, I was messing around with some other subcommands of the mmc command, and I ran "mmc rpmb read-counter /dev/mmcblk0", and it gave me some error saying that the ioctl couldn't be performed. Everything worked fine until I rebooted my laptop, and couldn't boot into my eMMC, and it didn't even show up in the EFI boot menu.

I can provide more info if needed, but I'm just wondering if there's a way to unbrick my eMMC.

might want to boot a live linux and see if you can access it by that means, or see if it will take a reinstall, without completing it. just see if it is letting you get to it and all of the steps before commenting to anything to destroy what is already on it. then maybe try to fix the uefi boot stuff.
maybe try,
supergrub2 on usb stick to see if it picks up the installed distro then boot into it via supergrub2 then fix your uefi boot sector.

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Every linux distro live disk I've tried fails to boot. I've tried alpine linux, gentoo and void. Each of the live disks booted into GRUB, but they all failed to boot during kernel initialization.

seriously, on a dell ? hum.. (redundant question) I assume you know what you're doing in creating a bootable live distro on a USB Stick, no matter what OS you're using to do so.

set BIOS back to default setting, if you now what you're doing to change it to something else, later. maybe try supergrub. if the mrb n your emmmc or it uses uefi ? supergrub2 also has a beta I think its beta out for UEFI as well that you might want to try. And if your biso is set up for uefi hopefully you're booting them live usb sticks accordingly as well. That might very well be the issue of a no boot. because you're just working off the BIOS and USB Stick. Not the hdd of whatever kind it is on the hardware.

I don't know about unbricking, but you might able to use it again after a re-installation. Check the UEFI settings, they might have been altered by the eMMC tools things you used. On my laptop I had to delete known keys to get anything DOS partitioned and bootable to show up in the UEFI list of bootable devices. In addition to enabling CMS / Legacy and disabling secure boot. I could change the latter two without deleting known keys, but they were reset upon reboot, so effectively not changed. They would not reset after deleting known keys and the changes would take.