Adam, I was able to solve the problem thanks to pelaird. I was just trying to find out which entry is responsible for making the missing group visible again, and thought this might help you investigate the issue further.
Since the missing group was also the default group “Pinned,” it’s very likely that it is related to the registry entry mentioned above, or to the setting “Pin Windows menu shortcut on Start11 menu.”
Anyway, I have now completely recreated the “Pinned” group and deleted the old original group.
Moving newly added pinned apps around is still a bit glitchy and doesn’t seem entirely stable. Otherwise, this wouldn’t have happened.
Best regards,
Thomas