Verify if your Apple TV app edition on Xiaomi TV is the full Apple TV app, or the specialized (but limited) Apple TV+ app (note the Plus in the app name and on the app icon).
One would have Store and Library options (and in-app third party channels), the other wouldn’t.
Unfortunately, that distinction is not user choice, but specific to the device model.
Get the Apple TV app or Apple TV+ app on your smart TV or third party streaming device - Apple Support
Apple TV app user guide for smart TVs and third party streaming devices - Apple Support

Users with unsupported TVs may consider getting a streaming device with the full Apple TV app. That can be an Apple TV box, Roku, Fire TV, PlayStation (4, 5), Xbox (One, One S, X, S), ‘Chromecast with Google TV’-dongle, or Nvidia Shield TV.