Why do you keep making things up, there is zero proof that osman was turkic.
"According to Ottoman tradition, Osman I, founder of Ottoman Empire, was descended from the Kayı tribe.[1][2][3][4] This claim has, however, been called into serious question by many modern historians. The only evidence for the Ottomans' Kayı descent came from genealogies written during the fifteenth century, more than a hundred years after the life of Osman. More significantly, the earliest genealogies written by the Ottomans did not include any reference to Kayı descent at all, indicating that it was fabricated at a later date."
They were from a region that arabs had previously devastated and fully conquered for hundreds of years. The osmans spoke Arabic and Persian, quit lying about them speaking Turkish I already gave you proof of this. Using common logic this implies arab fathers and Persian "mothers", something that would have been happening during and after the conquest of Iran.
As for mongols, they hated islam so that completely rules out turkish even being part mongol. The only (tiny amount) mongol dna you'll find there is from the few peaceful ones from byzantine or before and more from these:
https://en.m.wikipedia.org/wiki/Mongol_invasions_of_Anatolia
The osmans cared about tengrism yet inflicted islam upon Europe by the sword? Please check your logic. Let's see, which tribes were spreading Islam before? Which tribes wanted to break into byzantine before? As for surnames, of course they matter, MOST surnames are proof of an ancestral line, at least those who aren't stupidly religious. I haven't seen too many albanians with Asian, Greek or Slavic surnames. Those that have them may have had an ancestor from those regions at one point, also surnames tend to change slightly when in different languages/cultures for long period of time
But I am not here to speak about that, I want you, the expert, to find which haplogroup sub clades the arabs added to Iran, Syria after 650, that sort of region.