Well , except the pacman part. The chroot part should certainly work.

Yup. Mount your disk and chroot into it.

You may need to adapt the last part to your needs.

Example:

• for Fedora, you'd use dnf instead of pacman
• if your bootloader is broken, you'd want to run grub-install or grub-mkconfig
• if your initramfs doesn't recognize your new partition, you'd want to regenerate it with the current fstab or crypttab

I’ve never used Slax but it should, boot the liveUSB and enter terminal.

The general process is:

• Boot to live Slax
• Mount your install
• Mount /proc, /sys, /dev
• Enter the chroot
• Check if networking is working
• Attempt to run commands in your chroot
• Exit the chroot
• Unmount everything
• Boot back to your install

https://wiki.archlinux.org/title/Chroot

It should work, afaik chroot always use the binaries of the system you chrooted, so you will be able to use pacman normally. I don´t remember if chroot will mount the efi partition by default, you can do this before go to chroot (again, I'm have some memory issues but I believe that /dev does not mount as well if you just use chroot, this is why arch have arch-chroot that mounts this kind of stuff but you can mount before so it should work).

Assuming you are using systemd boot on efi partition (that is likelly if you have not changed the installer defaults), what I would do:

• On your live CD run sudo fdisk -l to get what is the efi partition, usually will be /dev/sdb1 since sda will be your usb, you should be able to see something like that.

• Then you will mount your endevour partition, in your situation should be sudo mount /dev/sdb2 /mnt/mydisk but check your fdisk command output.

• Now you will have to mount the efi partition sudo mount /dev/sdb1 /mnt/mydisk/efi

• Then you can use chroot /mnt/mydisk/ and proceed to do a pacman -Syu, this should trigger the post scripts that create the kernel images on the efi partition.

I'm sorry if I sounded insensitive, it wasn't my intention, just thought that since many others had already given a solution to the data and even OS recovery I could chip in to add something that they might find useful, if they don't mind switching away from Arch.
I hope mine would be a reassuring suggestion more than anything

Yeah you're right, however searching "linux distro with atomic updates" doesn't seem to turn up much, as you say, in most cases the two features happen to come together and the distros that have them are mostly known for the former

Yeah I know, that was a somewhat pretentious “backups” hint.