To watch AMC+ as tv channel through the Apple TV app, you will need an AMC+ subscription that is started in the Apple TV app. Subscriptions to AMC+ as started outside the Apple TV app are not valid for the tv channels.
Subscribe to Apple TV channels in the Apple TV app - Apple Support
Apple TV Channels FAQ: Services, pricing, availability, and everything else you need to know - Macworld
AMC+ tv channel requires sign-in to the Apple TV app on supported devices, and would then be automatic for subscribed channels.
AMC+ as started in the AMC+ app on Apple devices may not be recognized in the AMC+ app on third party streaming devices. To be multi-platform, subscribe with AMC+ directly.
AMC (linear TV) is different from AMC+ (VOD), with different plans.