Not only is it not a bug, the Home Assistant binding requires the MQTT binding. Until OH 5.1, the Home Assistant binding wasn’t a separate binding. It was packaged up with the MQTT binding. In OH 5.1, Home Assistant and Homie were pulled out and made a separate binding. But it still depends on MQTT being there.
With Home Assistant and Homie pulled out of the main MQTT binding, the main MQTT binding can now only automatically discover:
The MQTT binding can’t automatically discover anything else. And even for these, there are plans to split them out into separately installable bindings. If you don’t use these MQTT standards you can turn off automatic discovery as a setting on the MQTT Broker Thing (it’s the last property when you check “Show advanced”).
If there are Home Assistant Things in the Inbox that claim to come from the MQTT binding instead of the Home Assistant binding, then those Things were there before your upgrade. Perhaps they were ignored before and became unignored after the restore 
. They can be safely igniored now. The MQTT binding is no longer capable of discovering Home Assistant Things by itself. Only the newly separated Home Assistant binding can do that now.
There also could be something else going on. I think it’s the case that if you change the Thing ID after accepting them from the inbox than OH will discover that Thing again. So that could explain why Home Assistant Things are reappearing in the inbox.
But in all cases, no matter where the Things come from in the Inbox, if you’ve already accepted the Thing and they are working for you, you can ignore the new ones in the inbox.