Did you manage to get your system working again? Iirc I did the same on Arch a few years ago and it wasn't too bad to restore the system after looking at the permissions on a fresh install (maybe a container or vm, idr).
I tried. It was so long ago now I can't even remember. It was xubuntu, though.
But, I'm pretty sure I had to take it down to the local shop and get a copy of the iso since I didn't have a fresh install to compare. (This wasn't the only time I absolutely borked my machine)
Nowadays, I backup everything. I image the partitions. I create a separate partition for home. And I know what to never touch.
Agreed, backups are important. Before switching to NixOS (or image based OS like Fedora Silverblue) I made use of automatic btrfs snapshots. This makes these kinds of screw-ups simple to revert.
I'd like to say an overly optimistic chmod -R didn't happen again but my old Nextcloud instance would like a word.
Thanks for reminding to do my backups again. I've recently build a server with enough storage so I'll probably setup restic or borg. That means I can bring my external backup HDD over to my family as an offline/offsite backup.
I did something very similar while I was drunkenly troubleshooting issues on an old laptop and I gave up as soon as I saw the desktop going I just closed the lid and reformatted the next day