I do store regular backups of this machine, but not of /var. I can always reinstall Debian (or whatever other distro), while keeping other relevant configs intact (stored in the backups) and not lose any critical data.
I commented below that I did check /var/log/dpkg.log, but it didn’t help much due to the high number of packages removed that day.
At this point I am more curious to learn more about KDE and what is causing the problem, since other desktop environments (I installed mate) seem to work fine.