where has the home video tab under library gone?

If you are unsuccessful with the Computers app on the ATV note that another user is also having difficulty accessing home videos:

https://discussions.apple.com/thread/252254512

If this is the case I suspect it is a bug with Catalina/Big Sur providing Homesharing and you should consider submitting feedback to Apple

https://www.apple.com/feedback/appletv.html

(I am sticking with Mojave & iTunes )

On the Apple TV box, the Home Sharing video content can be accessed through the Computers app, not the Apple TV app.