I have HBO max and showtime with my internet and cable subscription

Unfortunately not. The subscriptions to Apple TV app Channels are a different kind of subscription, different perks and conditions, that have to be initiated and watched inside the Apple TV app. As such they are not exchangeable with subscriptions started outside the Apple TV app.

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