Instead of scrabbling desperately to take the effectively useless Hungary, the Ottomans focus on defending the Crimean Tatars and Astrakhan so they can finish the Don-Volga Canal. That gives them control of the Caspian. Persia is deprived of all of Azerbaijan and left an effective vassal. The western edge of Central Asia gets a smattering of Ottoman outposts.
From that position, Russia is kept from ever getting a substantial position in Siberia. This in turn makes them weak enough that Poland-Lithuania straggles into the modern era in a semifunctional form. The Turkic peoples in the West acknowledge theoretical Ottoman overlordship and send men off to fight for them in exchange for glory and loot. They also go home with modern weapons, which means that they are stronger than their neighbors to the east.... By the early 1800s, Central Asian is firmly in the Ottoman camp in the form of allied states that acknowledge Ottoman leadership as long as the point isn't pressed too hard.
With access to more useful troops and a lot less troublesome Christians to attempt to rule, the Ottoman low is largely avoided, though they'll have their ups and downs, I'm sure. By this time, it's safe to say history is well and truly off track, so it's not unreasonable to assume they've kept hold of Egypt and Tunis. Moreover, a more stable situation in the Balkans will let them get more entrenched. Thus more opportunistic conversions, more Muslim settlement, and less national consciousness.
Meanwhile, this Europe will be utterly unlike our own. If we assume a general war erupts in the 1800s and the Ottomans get involved, it's concievable that a fair portion of the male population of Central Asia could show up on horseback south of Kiev. Supported by a skilled and (relatively) up to date Ottoman army and assuming that it isn't a one front war....