AppleTV app on iPhone shows only "Library"

When I open the AppleTV app on my iPhone I get a screen with the heading "Library" and the text "No videos - your synced videos will appear here". That's it. No menu, no settings, no videos ... nada.

I have tried deleting and reinstalling the app, but it changes nothing.

It's been like this since the app first appeared on my iPhone. I've never been able to use it.

I would love to be able to watch or stream Apple TV content on my phone. Can someone help me understand what the problem is?