Here's what I'd say. I'm basing my predictions after rast's Great War Victory timeline, but after the Great War, the Ottomans would gain back most of the Arab peninsula, plus other regimes such as Yemen, Kuwait, Bahrain, Oman being subordinate states. The Ottomans would also likely get back Lybia from Italy in the treaty, with Egypt also being semi-autonomous. Azerbaijan is up in the air, as is Armenia.
I also say that they'd have trouble with the Greeks who get ideas about the Megali Idea, and that there would have to be a population transfer to get the Greeks out of the Ottoman Empire.
Then, the Ottomans would focus on modernizing, and they'd be able to get this done faster since oil is becoming more and more important, and they happen to have quite a bit of it now in OTL Kuwait and Saudi Arabia.
I'd assume Lybia would obtain its independance sooner or later, yet remain and ally of the Ottomans, while Egypt would gain full soverienty. However, the Ottoman Empire would keep its Arab provinces up to the present day, as more a Federation than an Empire.
Of course, there will be struggles and occasional rebellions along the way, but with the Middle East minus Persia united into a single Muslim state, we don't see the Sadaams, Osamas or other sort of bad people rear their ugly heads and would overall be more prosperous.