Called Apple Support. The problem was that the AirPlay 2 support was not activated. To get that activated, had to navigate to AirPlay and HomeKit then click on Room. That brought up a screen on tvOS prompting to activate BlueTooth on my iPhone. It took some work [1] to get that screen to go away, i.e. for the iOS to tvOS BT connection to occur but eventually the BT prompt screen did go away and then my HomeKit hub was shown on the AirPlay and HomeKit screen. It took another half hour or so for the iOS HomeKit app to connect, i.e. for HOME HUBS to appear on the Home app's screen which appears when you tap the house icon and for something other than a help screen to show up when pressing the Automation button.
[1] I don't remember exactly what magic finally worked. I think it was closing out and restarting the Settings and Home apps.