Once you pick from one of the mystery “home” or “mobile” or whatever contact methods for a person, you often get this screen, which makes it seem like you can press the main (touchpad) button on the remote to press the green button and initiate a FaceTime Video call. That is NOT the case.

Pressing the button on the remote actually moves the selection focus back to the user list! (You can figure out why if you look closely.)

If you actually manage to start a FaceTime call, it will periodically (every few minutes) be stopped entirely, displaying this baffling screen. The only possible action is to click the red “Disconnect” button.

After that, you have to reconnect Continuity Camera, which means getting up from the couch and picking up the phone to manually accept the connection, even though the phone and the Apple TV are both signed into the same Apple ID and the phone was already being used as a camera earlier.