There was a strange irregularity in the lower part in the passthrough hole (which is probably where my filament got stuck every time). Also the bottom opening was almost too tight to insert the PTFE tube (part of Bambu original). This might also have been the cause for the stuck filament.

I cut out the part with the irregular opening, scaled the lower part along the Z-axis to compensate and added a negative cilinder at the bottom for a bigger opening. Splitter works now for me.

I could only export as 3mf (3 objects), because export to STL in Bambu Studio drops the negative part (as does the Mesh Boolean function).