The bread is toasted. That is the German tell.
Berlin döner goes into a sturdy flatbread — pide, or sesame fladenbrot — pressed or toasted so it can hold meat, cabbage, tomato, onion, and sauce without collapsing. A Greek gyro uses a soft pita. Shawarma often uses a thin wrap or laffa. German döner uses a specific bread: pressed Turkish pide, not pita and not laffa. If the bread is a steamed pocket, you are not eating a German döner.
The bread is warm and sturdy enough to hold a full load. Sesame on the bread is common. Döner Haus pide is made only for us and shipped direct from Turkey. It contains gluten and sesame. The sandwich itself is not gluten-free, because the bread is wheat. The meat can be gluten-free if it has no wheat filler. Those are different claims. See meat and halal.
Three things made of wheat
Pressed pide, not pita
Pide
Turkish flatbread, sesame on top, pressed on a contact grill until it takes marks. Sturdy enough to hold meat, cabbage, tomato, onion and sauce without going through at the bottom.
The Berlin sandwich
Durum wrap
A flour tortilla with the same fillings, toasted on the same press. Travels better, holds less. A second build on one line, not a second menu.
Same line, same fillings
Pide quarters
The same bread sold as a side, the way a pizza place sells garlic knots. Not a Berlin requirement, and not something that goes inside the sandwich.
A side, not an upgrade
Some shops sell toasted pide quarters as a side, the way a pizza place sells garlic knots. Döner Haus does that. Extra bread does not go inside the sandwich. It is not a Berlin requirement. It is a good use of the same bread.
A durum-style wrap is a different item on the same line: the same meat, vegetables, and sauce in a toasted flour wrap. It travels well. It is still German döner fillings. It is not the Berlin pide sandwich. The wrap tortilla contains gluten.