I think support for iCloud services is no more for the Apple TV (3rd generation) (2012–2013) or earlier models (A1469 or earlier), due to changes in iCloud:
System requirements for iCloud - Apple Support
↳ Recommended: tvOS 17 or later (model A1625 or later).
↳ Family Sharing: tvOS 9 or later (model A1625 or later).
↳ iCloud Photos: tvOS 9.2 or later (model A1625 or later).
↳ iCloud Shared Photo Library: tvOS 16 or later (model A1625 or later).
Notably these changes to iCloud would be affecting this since 2023:
- My Photo Stream has been discontinued for all users.
- Advanced Data Protection for iCloud as an account property would invalidate some iCloud services on devices with older software.