you most likely need a backup of your /bin/,/lib/, /usr/ and /etc/ folders, because they contain files, essential for your system operation.
I guess we disagree about the point of backups then.
For me, backups are about data, as in, if I switch operating systems or something, it's what I'll need to get set up. /bin and /lib will just cause more problems than they solve since they likely won't be compatible w/ whatever system libraries are there. /usr is only relevant for the config files, and 90% of those are at whatever the distribution's defaults are (and on Arch, everything is in /usr anyway). /etc is useful for configs, but like /usr/etc, 90% of it is just defaults.
If I'm restoring from backup, I don't want to have random breakage, like config files, libraries, and binaries being incompatible. Most of the stuff outside /home is irrelevant, and the parts I do care about can be manually backed up through improving processes.
For example, I stick my self-hosted stuff into a git repo, and any changes I make get committed. I have scripts that deploy the changes wherever they need to go (e.g. I use quadlet, so this means systemd files), and those can be tweaked if something changes in a different OS. 99% of the things I host are containerized, so there is zero system-level impact (i.e. something that can't easily live in git or /home). For the rest, I largely accept that I'll probably have to fix a few things when restoring after an emergency , such as any configs for system services (e.g. /etc/sub(uid|gid), podman tweaks, users and groups, etc). I try to keep these changes extremely limited, and I keep notes in the README of my git repo, but it's never going to be 100% accurate since I often just want to get whatever it is working and promise that I'll update my docs later.
That said, the most important thing you can do, IMO, is test restoring from backup. I'm moving my systems toward containerization, which gives me a chance to fix all the stuff I totally forgot about. I keep the old system around for a while to reference (on an old drive or something), pulling files (and properly backing them up) as I go, and then I'll nuke it some months later. The important data is all in /home, which gets backed up, so it's mostly about service configuration (which I can look up later).
snapper
Snapper absolutely rocks. I'm spoiled on the openSUSE line of distributions that this is baked in. When an upgrade does sideways on my Tumbleweed desktop, I simply roll back and retry the upgrade in a couple days. It's magical.
snapborg
Looks really cool! I won't be backing up most of /, but I'll instead be a bit selective about which subvolumes I use. I already use btrfs everywhere, so this should be relatively drop-in.