Ok, here's what I tried:
Tilting and shaking the case, restarting the pump again and again, knocking on all the cooling components to get the air to come out of the system.
At first with the reservoir lid still on, but I couldn't see (or hear) any effect, so I took the lid of, drained a bit of fluid, did all of it again.
Booted the PC to make sure and no changes to the temps.
I took off the cpu cooler, cleaned off the paste, used a different one, used a little less, reattached the cooler.
To do so, I put the case horizontally on my desk and when I stood it up again, I saw that the reservoir looked full again (even after I had just drained a bit). When I turned the PC on, it emptied quickly again and I could hear a flushing(?) sound from the other components. So I'd wager that the radiator was full before, that's why I couldn't get any more air to come out.
After booting the temperature was again jumping between 30C and 50C per core.
I was kinda frustrated and went to get sth to eat, when I came back, the temperature had settled to ~25C.
I ran prime95 and after a few minutes the temperature rose to the low 60s where it seemed to stay, so I started to write this post and when I check again it had risen to 90° and which point I cancelled the stress test.
I kind of expected the cpu block or the pipe leading away from it to feel hot to the touch, but it's not even uncomfortable to touch. It feels slightly higher than room temperature. Is that normal? Or is that already a sign, that the heat doesn't transfer from cpu to the cooler?