I hooked Peacock to the Apple TV app, and while it shows my next playing episode, launching from the Apple TV app just launches the Peacock app, which feels rather pointless.
You have to subscribe with the Apple TV+ channel specifically for it to play in the Apple TV app (confusing, I know). Not all services offer a TV+ channel, unfortunately.
Hmm... I guess I'll check into that next time and pay more attention. I subscribed to Peacock+ through a bundle offer with Apple TV+, and went through Apple to trigger the purchase. It forced me over to Peacock to make an account there and other than billing it seemed totally separate.