Fixed the rattle. Hot glue gun did the trick!
I think I also figured out why it was rattling and why you, Serge, might actually not have the problem. The 3 bolts for SPD-SL road cleats are actually linked in a plate as well. It is just hard to see. If you look at the 2nd pic, my 2-bolt-plate sits below the 3-bolt-plate. If it would be the other way around (which I think would be the correct way to install them), the 2-bolt-plate would be clamped to the shoe when installing a road cleat and could not rattle at all. I think with my shoes they just installed them the wrong way around. Yours might not have the issue at all. The rattling is quite apparent and (for me) extremely bothersome. I think you would have instantly noticed if yours have the same issue (check video)

Just the usual shitty Chinese QC ...
Would be an easy fix to just swap them; sadly the base layer is glued/stitched to the frame so you cannot access it.