My gut says that that the Sublime Porte (whoever is running it) has bought themselves a decade to a generation as far as their European holdings are concerned. But obviously the basic demographics are against them, and Balkan nationalism isn't going away. Thrashing Christian minorities in obscure Anatolian hinterlands is one thing; trying to crack the whip on overwhelmingly Christian populations in Macedonia and Thrace is something else. The Bulgarians and Serbs are clearly reduced as threats for now, but that probably won't be the case forever. And if push comes to shove, Vienna and Budapest would surely rather have Balkan ambitions directed toward Turkish possessions rather than their own - if they can manage the process in an acceptable way.
Much will depend on how things develop in Constantinople. A strong nationalist military regime might be able to impose their will be force for a while (though it might also trigger full-scale rebellion). Chaotic developments will create opportunities for restive nationalist groups and neighbors.
With Russia reduced to marginal status for the next decade (or two) Austria will be the dominating power on the Balkans. Austria will allow the creation of "independent" nations on the Balkans instead of Ottoman Europe. But Austria will closely monitor that none of those nations becomes too big - sort of what Britain tried with the continent, prevent a domination nation that might become a future opponent.
Constantinople, Vienna---and Berlin. The flip side of my belief that AH will not disintegrate, because the most dominant German interest is to preserve it, also implies that in the end AH is a German protectorate. Not one without considerable say in its own fate, to be sure! They are "equal partners" the way the British Commonwealth was with the USA during the Cold War. A serious breach in policy between them would probably lead to the breakdown of AH, and enough dominant players in AH will understand that that they will, perhaps with a tight smile hiding gritted teeth in many cases, maintain the harmony.
And OE is the same sort of case I think--German interest favors keeping it all in one big package, especially keeping Mesopotamia (this may not be as obvious yet as it will become soon, but the region is valuable enough even without oil that the Germans will want to see it kept under the same ramshackle roof--and then the oil will be found and the stakes go higher).
The two client empires have obvious conflicts of interest; they will ultimately be mediated in Berlin.
Or of course German policy could slip and become less astute than it ought to be! Given the coming conservative ascendancy we've been promised, despite immediate factors my more romantic disposition suggested ought to block it, real stupidity is clearly an option. I suppose that when push comes to shove, given a less than deft handling of events combined with the balance of forces favoring disintegration versus unity in the two empires, if it comes down to having to betray or fail one or the other the Germans will prefer to favor Austria-Hungary. It is European, Christian, their neighbor, their close partner in a long hard war--OE is distant, Muslim, only a brief and peripheral partner. Of course they have all that oil! (If a possible crisis is delayed long enough for that to become a known factor). Perhaps that that point German policy would favor seeing OE break up and attempt to capture the Mesopotamian piece of it under some client regime--but doing that puts the region up for grabs, with British, and possibly French or American (via private channels as with Saudi Arabia in the interwar period OTL) and possibly even Russian tentacles getting into the game. Who knows, maybe the Japanese get involved? (Diplomatically, as fellow non-Christian, non-European outsiders appealing for unity against European hegemony?)
As a rule I think it is smart for Germany to preserve both empires. But if smarts fail, or outsmart themselves, I suppose OE would become a mess.
We have no author prophecy I recall on the matter. I'm going to call it as 50/50. A strong and well-run German hegemony can set the Empire on course for survival, perhaps with some negotiated and compensated withdrawal from the Balkans. Things can easily go wrong and a spectacular breakup and regrouping of influence channels would result.