Thx for this very helpful information ! After another successful test I have the same marks and they are indeed at the place where the tool is going down, I have this in all corners (not as bad as on the pictures as my material was only 9mm MDF instead of 22mm).
Looking at the machine very closely there is some flex in the gantry (no surprise to me) and in the bed holding the pieces (I didn't see this coming).
So I will have to make both of those stronger, but overall I'm *very* happy with my first piece (top part of a dust shoe héhé)