OK, so Mohammed was an Arab, Islam overcame the Turks and Arabic became part of the language and culture of the Turks.
I’m inclined to Tom Holland’s analysis that a character called Mohammad never existed.
Robert Spencer agrees with that
1. Mohammad is a title meaning the praiseworthy one. Nobody before the 8th century had that name.
2. The words Muhammad is used only 5 times in the Quran and only as a title
3. The Arabs conquered highly literate Persian Sassanid and Roman areas but there is no mention of a Muhammad in the first 100 years of the arab empire
4. They don’t even mention it themselves, not in their texts or inscriptions.
I think Muhammad was an amalgamation of many people like Robin hood
As to Islam overcame the turks, its complicated.
The original Turkic people in what is now Mongolia, were shamanism. Their kids were sold as slaves to the Abbassid caliphate and took back the religion. Then, in the 11th century the turkics took over Islam.
The major islamic powers: Ottoman, Safavid Iran and Moghul India all were Turkic dynasties. Though funnily enough, they used Farsi ie Persian as their court language