Good news, I did factory reset to the Apple TV and have done the setup from scratch manually and it is working fine! Thanks for sharing the solution!I’m on day four now of no issues and have been switching accounts regularly. I’d have to say I’m confident this issue is now fixed.
As you don’t have TestFlight I’d have to assume that didn’t have anything to do with it after all and Apple must have resolved this problem in an update without mentioning it in the releases notes and the fix didn’t kick in until a factory reset was done. It takes a bit of time but I’d recommend resetting yours and seeing how it goes as I haven’t had the problem since the factory reset.