Apparently this was not how you remove the doorbell from its mount. What is the function of the ripped off ribbon cable? The doorbell is still showing signs of life.
The reason I've asked this question is that it still shows all signs of life. Still detecting motion, door bell presses, camera is still online, there is still sound, it still runs on the battery... The only thing it didn't do was charge via the cables in my wall (but that was the reason I tried taking it off in the first place so I can't say if that's because of that ribbon cable).
If anyone is interested: I fixed it. Bought one from eBay that was listed for parts and took out the component that had the ribbon cable soldered to it. Just had to attach it to my one and done! All in all an easy fix (if you can find that part). Saved me at least 100 euros.
FYI: that ribbon cable is not responsible for any functionality of the doorbell. It takes care of everything related to charging the battery.