The Homekit App on my iPhone says "Home hub not connected"

The Homekit App on my iPhone says "Home hub not connected."

On my Apple TV, in Settings -> Airplay and Homekit -> Home Hub

It says "Connected."

I dried disconnecting, logging my account out of iCloud on the Apple TV, restarting the Apple TV, logging back into iCloud, and turning the AppleTV back into a Home Hub again. Again, it says "Connected." It still shows "Home hub not connected" on my phone.

I tried quitting and restarting the Home app on my phone, and restarting the phone - I still get "Home hub not connected."

The phone is on the home Wifi network, the AppleTV is on Ethernet to the same router. The setup had been working fine for years.

I use Home Sharing to my Wife's account, so I borrowed her iPod Touch. In the Home App on her iPod, it does NOT show "Home hub not connected." It lets me make and edit automations. These automations work. So the Apple TV is right, when it says "Connected." It's my phone that's wrong when it says "Home hub not connected."

I created a new home automation on her iPod, and that new automation immediately popped up under Automations on my iPhone - so my iPhone would seem to be connected and getting new Home information from the AppleTV as a home hub? But on my phone, I can't create or edit Automations, because it says "Home hub not connected."

What next?