I can't screen share Showtime on my Apple TV

the pictures disappears and the sound continues

Early Apple TV model

Note that the Apple TV app Channels are not supported for AirPlay to an Apple TV (2nd generation) [A1378], if that is what you have. Audio without video is expected in such a situation.

Some streaming app removed airplay support due to their own policy, and wants users to use the app on the device.

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

Are you trying to AirPlay screen mirror from your Mac, or from a different device?