Does Apple TV support screen rotation on iPhone 15 Pro?

What do you mean "how"? Just rotate the phone so you're viewing it on its side and the screen's image will turn likewise.

If you mean something else please elaborate with details after reading the following guidelines on how to ask a question:

Writing an effective Apple Support Commun… - Apple Community

… unless you have the rotation lock toggle active. Then the TV app won’t rotate, of course.

Rotate the screen on your iPhone or iPod touch - Apple Support

If you mean will the movies you want to watch rotate to landscape mode on the phone the answer is yes.