I've yet to fly the Mini 3 with it now being registered. I received the Plus battery yesterday evening and it was raining here, so I'm currently in a hold pattern for flight.
I did test the Plus battery, though. Mine is NOT a DJI branded Plus battery, but it still shows extended capacity. One thing that threw me is that I was trying to determine if Remote ID was enabled and broadcasting. I did notice that the Flight Checklist shows, "Remote ID functionality normal (code: 1B080003)" within the remote controller UI. I also tested to see if that disappears when I use the normal batteries - it does. Based on that, I'm assuming that the Remote ID is being broadcasted.
As well, I went ahead and bought a Remote ID broadcasting module so that I can use the non-Plus batteries.
I've noticed that it's clear skies right now and it's 5 PM EST, so it looks like I'll be able to conduct a dusk test flight today!