Apple TV not working or showing anything on screen

Could it be that your Apple Account is set for a country or country-like region where Apple doesn’t offer any video services?

Availability of Apple Media Services (by country) - Apple Support

Then the Apple TV app would only show a Library for local videos that the user optionally adds themselves.

If the country or region for your Apple Account is somehow misaligned or mismatched (different from intended), then you can reset it correctly, by signing out, and then signing in again.

You can sign out and sign in for the app from the menu bar at the top of the screen, through the Account menu.

You can also sign in or change accounts from the Apple Account option at the bottom of the side bar.

The Apple TV app doesn’t have to be in Full Screen mode, which may help you to see options (menu bar) better. The viewer window for watching content has a separate full screen option (⤢).