Do I have an Apple TV account ?

There is no such thing as an Apple TV account. Users of Apple devices and services have an Apple ID account. That Apple ID account represents the user, an individual, and they may use that account on multiple devices. You can have services (subscriptions, digital purchases) linked to that Apple ID account, such as Apple TV+ (subscription) or iTunes Store movies (buy or rent).

You would have an Apple TV+ subscription, if you signed up for that. It isn’t automatic.

See your subscriptions overview - Apple