Apple TV mirroring from iPhone13

See here: Use AirPlay to stream video or mirror the screen of your iPhone, iPad, or iPod touch - Apple Support

For apps that have in-app AirPlay controls, use that.

For other apps, use Screen Mirroring in Control Center.

If you run into trouble, read here: If screen mirroring or streaming isn't working on your AirPlay-compatible device - Apple Support Some content providers (apps) don’t make AirPlay accommodations. A few content providers block their content from AirPlay use. That is their prerogative.

Connect the TV and your iPhone to the same network and the go to your settings on your TV and click on my iPhone the from your phone tap on screen mirror! Hope this help🤩🤩