Sorry for getting back to this so late.
I diagnosed that it is probably DCS blocking Windows from seeing the Windows key is pressed. Weird that it only happens with the headset on my head.
The solution was very simple: I put a piece of tape over the little green LED and proximity sensor between the lenses so it does not sense when I put my HMD on and thus does not trigger the problematic behaviour. Have been DCS’ing without problems since