@primoz.rome, thanks for the recording! That was very helpful.
I’m not sure whether this is a bug, oversight, or something else, but I’ll report it to the devs and let you know what they say!
After some investigation, it seems to me that this has nothing to do with the Auto-save plugin per se (as you hinted at), but is actually due to the multi-link field (Pages) being set up to use the “Expanded view” field editor:
If you switch it to Compact view, saving (whether manual or automatic) won’t close the popup editor anymore. Of course, this isn’t a great editor experience when you have a lot of pages (blurred for privacy):
If you want to try it for yourself, I forked your main environment into something called datocms-support-main-new-copy-2023-11-21.
Again, I’m not sure if this is intentional behavior (seems odd for it to be), but I’ll let you know what the devs say after they look into it.