Apple TV isn’t showing up on screen mirroring

do the remote app works?

because if it aldo does not work then maybe your router is not set to bridge 2.4Ghz 5Ghz and wired ethernet so if

the iphone does not connect to the same network as the appletv they can't see eachother and of cause

airplay do not work over the internet so the iphone needs to be on the LAN

What is your model Apple TV? Identify your Apple TV model - Apple Support

Is the Apple TV box functional for streaming directly? If not, then that may affect AirPlay as well.

I set up Apple TV but when I try to mirror, this device doesn’t show as an option to select