Thanks again for your help. But I'm pretty sure you misunderstood me because of my bad Englisch (sorry, German here). So I made two photos. One with the sleep setting with 1 minute auto off and disabled sleep timer and the other photo is what happens after the 1 minute of the auto off elapsed
One more time: The screen of the second photo appears AFTER the 1 minute of the auto off setting elapsed. To wake it I have to press the power button a long time, a shot press does not work. So this is not just switching off the screen and then waking it by a short press. Anyway, this behavior NOT CONSISTENT when I unplug the headphones while the PD plays a song and it paused the playback because of the unplugging. However, the behavior IS CONSISTENT as I expect it whenever I manually pause the playback whether headphones are plugged in or not. Then it goes to sleep mode. It appears to me that this inconsistent behavior of going to sleep or not going to sleep after the set time is dependent on the headphones I use and then unplug. Or it may dependent on how fast or straight I unplug them. I know this sounds ridiculous and I sincerely hope I did not misunderstand you but I can tell that at least my PD behaves strange when it comes to going to sleep.
(And as far as I understand it the sleep timer – or in my picture the "Ausschalt-Timer" – is for going to sleep at night and force the player to shut down no matter what after 10 to 120 minutes like setting a timer for a TV in case you fall asleep while watching it. Sorry again for my bad English. I hope you know what I mean.)
Have you reset it yet?