Chosen Solution
I replaced my display with an Ifixit replacement part and I did put in a new battery. Everything worked fine (it is the 3rd time on this phone) After a while I realized, that the display was showing some flickering which can barely be noticed. I turned the brightness up and down to see if it would went away and then it got so dark that I couldn’t turn it bright again. After I finally got it back lighted I turned of the brightness adaption and rebooted several times. When closing the phone everything seemed connected well. There has been a screw - right above the Wifi-Cable connector which seemed loos and I tightened it. Don’t know what to check for. The display goes dark, as soon as I turn down the brightness to 25-30%
It sounds like a defective screen, screen should not go extremely dark, contact iFixit about the issue and see if it qualifies for a warranty replacement.