Family Sharing Premier plan

You are referring to the Apple One premier plan, which has the 2TB iCloud+ shared storage space.

Other services available to all family members are Apple Music, Apple TV+, Apple Arcade, Apple News+ and Apple Fitness+

See the note towards the foot of the Apple One page: If you have the Apple One Family or Premier plan, you can use Family Sharing to share all included Apple services with up to five other family members. And Apple TV+ and Apple Arcade always include Family Sharing, even in the Apple One Individual plan. Learn more about Family Sharing

See also Use iCloud with your family

Your selectivity options with family sharing are limited but you do have some. In particular note the section quoted below from How to share purchases with your family - Apple Support

"When purchase sharing is turned off, you can continue to share subscriptions like Apple TV+ and Apple Arcade."

To me it sounds like that may accomplish what you desire in as much as AppleTV goes.