I manage to get some screenshots to visualize my issue.
The Apple TV name is 'CRISTINA'.
1 Ipad IOS 17.0.3
Sometimes the name of Apple TV appeared under Screen Mirror, sometimes Not. It is very strange I was able to mirror to Apple TV my screen from Ipad watch a movie and after that the option of mirroring was gone.
When I check the remote control option from Control Panel the name of Apple TV is there.
2 Iphone SE IOS 17.0.3
Better behavior, the name Apple TV show-up on both mirror and remote control option from Control Panel.
I powered off all my devices and restart them, same behavior for the Ipad.
Looks like I'm not able to attached the screenshots ( this site don't allowed because of the size).
Can you give me another option to send you the screen shoots.