I have concluded I just don't understand how the custom sort values settings work.
I selected a track from the album shown on the left, and selected
Edit Custom Sort Values in the
Tag Editor.
It showed these three values:

I did the same for the one track in the album shown on the right, and it showed an additional entry with the space between the names missing:

I've never had any
Sort Artist / Artist Sort or equivalent tags in these files so I don't know where they came from.
If I delete all the values from those settings from all the tracks, they just repopulate again when I re-open the dialog.
[Update]
Success! Sort of.
I was able to fix it by selecting all tracks and using the
Artist Splitter in the
Tag Editor to explicitly set the
Display Artist to both names separated by a space and semi-colon:

Mp3tag shows this added a Display Composer tag too.

What's weird is that if I delete these two Display tags in Mp3tag now and then rescan them in MusicBee, the tracks still appear correctly as a single album.
So I do wonder if MusicBee isn't doing some caching or somehow not updating those values when the tag values are changed via the
Sorting tab in the
Tag Editor.
Or as mentioned, I don't understand how those settings are supposed to work.
It's a bit confusing the way those settings in the
Tag Editor overlap with some but not all of the same settings in the
Preferences.
Thankfully, I only had to fix one album. Not sure if the suggestion to update tag values en masse using the Tagging plug-in will work for the OP.
I've ended up with the same tag values as when I started, so it still doesn't appear to be solely a tagging issue.