I noticed something else that ultimately led me to a workaround. If I activate the screen saver immediately after closing a video streaming app (using the back button on the home screen), the screen saver appears and then disappears again after a few seconds. If I press the back button again, the screen saver remains active. This indicates that a few seconds after closing an app, the Apple TV device does something else and thereby activates the home screen again or something similar. Workaround: What I do now is press the home button once and then wait 5-10 seconds. Only then do I turn off the Apple TV and devices connected via HDMI using the power button on the Siri remote control. Then the error does not occur.