MacBook A1534 Early 2015 12" with flickering lines

I have a MacBook which started to act strange when I upgraded to Catalina.

The screen shows scrambled lines, which started with a misaligned and green screen.

I've done all the resets, re-installations, downgrade to the previous OS, etc... without any success.

When I attach an external screen it all works fine, also at startup until I enter my password and press enter.

same as described here: https://discussions.apple.com/thread/251268846?login=true

Any suggestions?