Cannot log in to Apple TV+ on my smart TV. Is it $5 per TV per month?

So frustrated here. I have a paid subscription to Apple TV+ and went to watch my fave show in another room for the first time. It's a Samsung smart TV.

I found the Apple TV+ app in the menu, but THERE WAS NOWHERE TO LOG IN on the Samsung smart TV. Instead, its Apple TV+ app insisted on making me sign up for a new subscription. Grrrrrrrr!

I know you can log in on an iPad, Android, or Windows via iTunes. But no login is visible on this Samsung smart TV. It really stinks.

Does this mean it's $5 per month per TV, or is it an error with Samsung? That seems wrong if each TV has to have its own subscription, but if so, and they should at least disclose that promintently on the app itself.

WHY IS THERE NOT EVEN A LOGIN on our other smart TV?