My movies will not load on the Apple TV App

The Apple TV+ app on TV provider equipment is a specialized edition of the full Apple TV app, bringing access to Apple TV+ subscription content (and FNB and MLS). However, it lacks a Store and Library tab for access to purchased or rented movies from the iTunes Store. It also doesn’t have third party in-app channels. To include those, you’ll need the full Apple TV app on different supported devices (Apple TV box, Roku, Fire TV, PlayStation, Xbox, Nvidia Shield, ‘Chromecast with Google TV’ dongle, or select smart TVs).

This support document has more information of the differences:

Get the Apple TV app or Apple TV+ app on your smart TV or streaming device - Apple Support

List of devices to watch on smart TVs and streaming devices - Apple Support