tvOS 16 has the following problems:-
After the update, all accounts need additional 'configuration' and the only option is to use an iPhone/iPad running ?OS16 (despite iPadOS 16 not having been released at the time). There is NO option to enter anything manually so any AppleTV accounts that are not also used as a main iCloud account on any other very recent device CANNOT be updated in tvOS 16 and therefore the big red flag remains in settings with iCloud features not working for that account.
On waking the AppleTV, the screen shows 2 buttons to 'View new Terms and Conditions' and 'Not now'. The first option just takes you to a screen with a single option - 'Sign out', so no viewing any T&Cs at all. The second option just repeats the process and the same screen is displayed again. Selecting 'Not now' a second time seems to finally clear this - until the next time you try to use the AppleTV.
If in order to clear the annoying red flag claiming additional setup is required (only by iDevice running ?OS 16) you sign out of the main iCloud account and back in again, you WILL be presented with the new T&Cs and henceforth not be troubled by that irritating demand that takes you to the wrong place. However, not only is the same red flag still showing against the account, but now the Apple TV is no longer part of your HomeKit setup and that can ONLY be set up again using, you guessed it, an iPhone running under that same account. However, the good news is that in this case there is no apparent requirement that the iDevice used to do this is running ?OS 16. The bad news is that using an iPhone running iOS 15 seems at first to be working, but the Apple TV simply goes into some perpetual loop with a spinning daisy wheel and when you eventually back out of that (using the Menu button), you'll see that 'Home' is still not set up. But…
After sleeping for a few hours, on waking the Apple TV I found no more red flag notifications about more set up required for any accounts and even the Home(Kit) setup has now in fact miraculously been completed. However, at the top of each AppleTV account's page it still shows at the top
'Finish Signing In with iPhone'
even when there is no red notification flag indicating something actually needs to be done. So is it actually complete or does it still require something more? Needless to say, clicking that line above takes you to where it asks you to complete setup using an iPhone/iPad (?OS 16 only) and NO manual option. But since there was no red flag, does it really need anything? Talk about 'ambiguous'.
So to sum up, it's a complete and utter mess. If you've not yet updated to tvOS 16 and don't have another iDevice running ?OS 16 for each of the AppleTV accounts, I'd suggest you don't update. Wait until these major bugs have been quashed and save your hair.
I took this up with Apple who admitted they are seeing many reports of such behaviour, so they are aware of it, but the not so great news is that we'll just have to wait for a tvOS update to fix it and there's an iOS update to release first. Fortunately, in the meantime, at least the AppleTV can still be used to watch TV.