No. I cannot connect to the HomePod minis - I can see them just fine. Instead, I get this infuriating message.

So far I have:
- rest the HomePod minis
- reset the AppleTV
- removed all of them and re-added them to the home
- removed and added them to different rooms
The only thing I haven't done is created an entirely new home, since that means all of my devices have to be reconnected which seems insane for something that worked just fine .1 ago.
This misbehaving setup is in the bedroom, to explain the next part.
Even more insane, if I stream to the AppleTV in the basement, say using Music on the AppleTV in the bedroom, I can also then stream to the AirPods in the bedroom. However, the second I remove the AppleTV in the basement as a streaming option, it stops being able to stream to the bedroom. I can't select it.