--- Comment #1 from Lars Marowsky-Bree email@example.com --- I had played with xrandr --off / --auto for a while for that output (turning the monitor's power on/off etc as well), and then eventually gave up and turned the display off.
After ~2h hours, I decided to give it another try, turned on the monitor, and ran xrandr --output DP4 --auto again. (A sequence I had done multiple times before). Lo and behold, this time, the monitor came online fine and is now displaying.
I don't know why, and I don't really trust the result ;-) It was also not reproducible, there's nothing new in the logs from either X or in dmesg. I can't tell what is different now.