On what brand and model TV is this? Do you know the year of model introduction?
Some select TVs (and select third party streaming devices) get a specialized edition of the Apple TV app, and named slightly different to reflect that: Apple TV+ app. This edition doesn’t have a Store, nor Library, nor options for third party channels. Could that be it?
Get the Apple TV app or Apple TV+ app on your smart TV or streaming device - Apple Support
Apple TV app (and Apple TV+ app) user guide for smart TVs and third party streaming devices - Apple Support

Users with TVs that do not have support for the full Apple TV app, can consider an external streaming device that does support this bigger edition. That can be an Apple TV box, Roku, Fire TV, PlayStation (4, 5), Xbox (One, One S, X, S), ‘Chromecast with Google TV’-dongle, Nvidia Shield TV box.