Eh, it depends. Several Kurdish tribes fought for Russia in the wars, and many others stayed neutral instead of joining the Ottoman side like they were formally expected to. There was even some small-scale migration of Kurds from Ottoman lands to the Russian Empire. Kurdistan wouldn't pose much of a problem to Russian influence or puppetization - for as long as they have the wisdom to keep Kurdish traditional structures in place and work through them.
So I believe Russia could annex much of eastern Anatolia (with Kurdistan preferably as a protectorate, not annexed), as well as the OTL Romanian and Bulgarian coastline down to Constantinople. Constantinople is where it gets tricky, because going for Constantinople will cause an extremely negative reaction in one or more of Russia's fellow great powers. There may be opportunities to seize it, but it would have to be very well timed and planned out. The rest of the Balkans - Romania, Bulgaria, Serbia, maybe Greece...could become Russian allies or protectorates. Not sure that Russia would necessarily be interested in allowing Greece to expand into Anatolia, but who knows.