And... We have something that resembles an answer. It's not intuitive, so hopefully anyone else with a similar situation will find this helpful.
First, we disconnected my wife's phone and iPad Pro from our network. Then we restarted both the HomePod and HomePod Mini. Not reset -- just restart. Then we reconnected the phone and iPP -- and waited overnight. At that point, they started talking to each other again.
After some testing, it seems that HomeKit's taking hours to fully link changes back into a functional system. Add a user to the Home, and wait. Get an error -- disconnect the affected devices, restart them, and wait. All the misbehaving phones, iPads, and HomePods have to disconnect from the network, sit for a bit, then reconnect. After an indecently long interval, it all works again.
No idea why. But at least we're working again. YMMV
02-07-2021 04:36 PM