I say they should be European, since the majority of their original conquests are in Europe and since their capital, Constantinople/Istanbul is in Europe, they should technically be European BUT I think they need all their stuff reworked. Their houses need to look unique, their town centers need to change. They should not share the Spanish-Portuguese architecture. Their civilians are fine since most Ottomans, regardless of ethnicity or religion, covered their hair.
But…I think they should actually have a consulate and possible wonders since by the 1700s, the French, Germanic peoples, Swedes, and Russians all began to actively seek treaties to exploit the Ottomans. If I we went that route, they could have Sultan Ahmet Mosque (Blue Mosque) as a wonder, Topkapi Palace, Suleymaniye Mosque, Dolmabahce Palace, and I don’t know, um, I forget the fortress built outside Edirne, the one the Ottomans used against the Byzantines.
Also their units need renamed. Abus Gunner to Cebeci, the Bostanci should actually be heavy infantry, like pikemen, their “hussars” should be either Akinci or Deli light cavalry. Actually, no, Deli should be their hussar replacement and Akinci should be their cavalry archers. Keep Sipahi and Janissaries the same. Although the correct spelling of Janissary…lol.