Ok, thanks for yoru feedback again.
I think I found the problem.
The automatic bridge itself is ever so slightly touching the balance.... to be precise the lower bridge. The upper bridge is fine and doesn't touch the seconds spring (which is brand new and ever so slightly lubricated on the contact point).
If I install the bridge without all the wheels (upper and lower bridge combined; even without the rotor axle) , the amplitude still drops. See picture (where you see the exposed seconds spring).
But if I install the upper bridge without the lower bridge, everything is fine.
I'm not sure why, though. Maybe the piece itself is a bit bent (even though it looks fine). I ordered a replacement and hope that this will solve it. The tolerances must be ridiculously tiny (between the bridge and balance).
I'll report back...