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The Apple TV app Channels require a subscription that has been started in the Apple TV app. These would not be exchangeable with existing subscriptions started elsewhere. If you switch to an Apple TV app Channel subscription, then most often you are required to view in the Apple TV app, unless the original content provider has made provisions for use outside the Apple TV app (like CBS has done).

Apple TV Channels FAQ: Services, pricing, availability, and everything else you need to know - Macworld

Subscribe to Apple TV channels in the Apple TV app - Apple Support

You would have more flexibility with an Apple TV set-top box, which allow one to install a separate third party app with it own sign in options. Or one of their other supported streaming devices.

You would download the app from the on-device App Store, open it, and look for a sign-in option. If you can’t find that option, then consult with the developer/publisher of that app. How to contact an app developer - Apple Support