FIXED IT!
I have two monitors, both on DisplayPort. My primary display blacks out / turns off at random moments, and you can hear the notification sound that a hardware device is removed, force pushing all my active windows to the other display. Less than annoying when I'm doing office work, more so when I'm gaming.
Initially I thought it was the GPU - and everyone on the internet suggested so - but nothing in the logs showed that and everything graphical works fine actually.
Then I figured, since I game on the primary display, I need to swap it with the secondary display so if the primary blacks out, at least I don't need to turn my head to the secondary, waiting for it to switch my active window back to the primary. I wanted to physically swap the displays, believing the monitor was faulty, so I pulled out the power cable and the Displ.. Wait, I need to isolate the PSU first and check that. And without physically swapping the monitors, I only swapped the PSU plug that goes into the monitor.
That's how I finally found out that the culprit was the power supply unit: the cable that plugs into the monitor was chewed on by one of my cats, barely visible. Indeed, now the other, secondary display blacks out. There's nothing wrong with either monitors. And when it does happen I only need to wiggle that chewed part a bit and I can force the display to turn on again. FFS. I ordered one new PSU.