Unable to access my Apple TV+ library

Some (mostly newer) TVs get the full Apple TV app, while some other (mostly slightly older) TVs get the specialized Apple TV+ app (with the Plus in the name and on the tile). As negotiated between Apple and the device manufacturer; unfortunately not user choice. The latter has a few functions left out, including the Library.

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

TVs without the full Apple TV app could connect an external streaming device that supports the full Apple TV app. E.g. Apple TV box, Roku, Fire TV, PlayStation (4, 5), Xbox (One, One S, X, S), ‘Chromecast with Google TV’-dongle, Nvidia Shield TV box.

I think Apple TV+ and Apple Music is down for some users. I couldn't download Atmos and Lossless w/o getting bombarded by Network errors even though my network has no issues.

Apple - Support - System Status

Yes, I have read your post and I am saying Apple TV+ and Apple Music both were affected in a service outage. You gotta read before making assumptions.

The service for Apple TV+ should be fixed by now.