After a weekend I can say, that the version from July works like a charm.
So I’d recommend downgrading the server (see @badelie’s guide Server disconnects - Screen goes black during playback - #3 by badelie) for now.
I’ve also noticed that Plex hasn’t synced my watch state since ~mid October.
After downgrading it synced >80 entries for my user only (having multiple users = a lot of watched entries).
Uptime reached 100% again except for yesterday when it crashed once due to freezing when I started an episode, which happens from time to time.