If your Apple TV is a 3.9" black box, then it is at least 2nd generation.
If your Apple TV is a 7.7" white/aluminum box, then it is 1st generation.
Identify your Apple TV model - Apple Support
Many on this forum have misidentified their older model, hence my request for confirmation.
To sign in on your 2nd or 3rd generation Apple TV, while having two-factor authentication active, requires a bit of an adjustment for the procedure. Please see: https://discussions.apple.com/thread/250420575.
The Apple TV (1st generation) can no longer connect to the iTunes Store, and can no longer sync with modern iTunes versions. It is obsolete from both a support point of view, as well as practically.