Pegasus Airlines denied me boarding in Istanbul despite my German urgent passport and approved Azerbaijani…

Hi everyone,
I'm a German citizen, and I recently had to obtain a German provisional passport (Vorläufiger Reisepass), which was issued today and is valid for one year.
Before travelling, I applied for a 3-month Azerbaijani e-visa and received approval.
I booked a single itinerary with Pegasus Airlines: Cologne → Istanbul → Baku.
I travelled from Cologne to Istanbul without any problems. However, when I arrived…