Apple TV subscription

No problem.

The first episode doesn't require any subscription, its available to any user as a way to preview a show before signing up, that is why I wanted to make sure you still had an active subscription.

You should also check that the app has properly been logged in with that same account (it's not automatic), otherwise you won't be able to access that subscription. If it was already logged in you can try signing out and log in again.

Apple TV Plus can be accessed on any device that has the Apple TV app. However, casting can only be done via airplay. This means sending from an Apple device, to a smart TV (with airplay support), Roku, or Apple TV box.

To see the full list of supported devices

Apple TV app - Devices - Apple (EG)

First episodes are usually available without a subscription. Check your account to ensure the subscription is active, and that you are logged in with that same account via the app. If verified and the issue persists, first try deleting and reinstalling the app and then contact Apple support.