I took my MX Master 2S apart from cleaning and everything went well. Sadly a new issue arose when putting it back...

So after all, the gesture button (where your thumb rests on) was constantly pressing the gesture function of the mouse, deactivating mouse movement. Looking further into the “constantly pressing Gesture Button” issue, i found out that it seems to be a quite common defect. While some people seem to just cut of the button entirely, you can also deactivate the Gesture function completely in the Logitech options software. Turning the Gesture Button PCB around fixes the issue completely and retains functionality, i found it out by trial and error. I hope this can help someone else in the future aswell, the plastic mechanism holding the rubber away from the button seems to weaken over the years. Anyways, thanks for the help, iFixit is the best :)