Family Sharing is for sharing between accounts (different users).
Any Apple TV app user can access purchased content on any of their devices, when signed in with the same Apple ID account to the Apple TV app, without need for Family Sharing.
Family Sharing only allows the sharing of purchased movies, if the Purchase Sharing option is activated. Activating Purchase Sharing will also charge any new purchase from any of the group to the Family Sharing organizer’s payment method. That may or may not be desirable for every group.
Access shared purchases through the Library tab, then Family Sharing, then user.
Family Sharing - Apple
What is Family Sharing? - Apple Support
Set up Family Sharing - Apple Support
What types of content can I share with my family? - Apple Support
↳ Notably movie rentals are not shareable.
How to share purchases with your family - Apple Support
If you can't find your family's shared content - Apple Support