I did contact Apple from the links you provided and got to a very helpful person on the phone. She had to research it and find out why. The answer is just what we suspected: they have updated the Apple TV to 16 and it will only talk to an iPhone or iPAD with iOS 16 or better. I have an iPhone SE iOS 14.4. that cannot even get to iOS 16. No going backwards on the Apple TV, no substituting another person instead of me because it can never get a code for permission to make any changes. When I am finally tired of having an out of date iPhone and forced to get a new one, perhaps it will have an iOS compatible with the lastest update on my Apple TV. Their loss. We do not buy anything on Apple TV and don't need any Apple ID codes to function. And this cinches it.
Thank you for your help. Pass the word.