The show was Ted Lasso
I got this message on several episodes of Ted Lasso, and on the movie Tetris.
All the content works fine on another (poorer) device, on the same internet connection
I don't know how to do 1-3 of your list of 1-4. I'll see if I can check the time zone thing tomorrow. It seems unlikely that would be the problem, though, because no one changed the TV's time zone setting while I was watching a show.
I can also look into 1, 3, and 5 of your list of 1-5 tomorrow. Realistically, though, I will probably just keep watching Ted Lasso on my poorer device until it ends, and then unsubscribe from AppleTV. I appreciate your help (and I see that you've advised other people who have had the same problem I have) but I have five other streaming services that work just fine on my big tv.