Could check with standard #6, #8, or #10 screw (these are 32TPI) and aligning up the crests. Might need a magnifier to get into the tight spaces.

Geez, my bad. You’re in Germany so those screws wouldn’t be readily available. Perhaps from some US made item, just provisional borrowing.

Addendum:
Don’t mean to be condescent, but a set of screw pitch gages saves the day (Link to Ali Ex). Machinist by trade and had a few surprises with some of the in-house threads – flashlights and other things. Also a digital caliper is essential in measurement (link Ali Ex ).