Feb 22 2021
@Srdjan and I did some testing (see https://bs.wikipedia.org/wiki/Posebno:Doprinos/Blablubbs) -- I can move pages fine both with and without the autoreview flag, so assigned user groups don't seem to be the cause.
Feb 21 2021
@ppelberg I've given it a couple days to see that it's working reliably, and indeed it is. I think this can be closed -- thanks for the fix :).
Feb 3 2021
Well, sorry for the spam but it's broken again. I'll just report back once it's been working consistently for a couple days.
Feb 2 2021
Update 2: Has since dropped in and out a couple times, but has been functioning consistently today -- I assume the fix was pushed and is working. @ppelberg Thanks for fixing this so quickly, I think the issue can be closed.
Jan 29 2021
Update: Now started working again.
Jan 28 2021
Will do @ppelberg; thanks for the quick response!
Jan 27 2021
Indeed, that was the edit -- I had enabled enterprisey's reply-link for a while and just uncommented the line so I could just wait and see when it would start working again. Some time after uncommenting, it actually worked for a bit -- see e.g. the tags here https://en.wikipedia.org/w/index.php?title=User_talk:Blablubbs&diff=prev&oldid=1002953117. I'll keep you up to date in case it unbreaks again.
The patch appears to have fixed the issue for a short while, but it looks like it broke again - at least for me.