I'm wary of giving advice because I haven't done it before.
Anyway, I think you'd have to boot the live media, and properly restore the @_backup_20220112230608429 as @, then fix the grub and fstab entries if they still refer to the backup. Then reboot, update, reboot, and update remote reset-snapper.
Apologies in advance for the hand waving.
This thread was a similar case with a "sticky" snapshot, maybe there is some useful insight there.
There are likely other threads with a similar problem.
If you're considering a reinstall anyway (yes, keeping the two on separate drives is safer) you sort of have nothing to lose trying, just make sure your data is safe (backup that is).
For information, as far as I can tell there are two kinds of snapshots that are made automatically: the ones in .snapshots, taken pre/post package manager operations and/or periodically, and those named something with _backup_ and a timestamp in the name, taken before restoring one of the "regular" ones.
Apparently the snapper tools only manage the ones in .snapshots, not the "one off" kind.
After all they could be anything.