The wargamer in me would had liked the Greek border not to extend north to Propontis and go further east to make it more defensible instead but I expect Venizelos would had based his final claims in 1922 upon his claims in the 1919 peace conference. Which from an economic and population point of view would make sense. That said I would not assume Greece gets the region by default. If it does it controls both ends of the straits. Britain may like this. The Soviet Union will definitely not.
I mean, compared to the rest of the claims on Anatolia, easily the least hard fought to pressure Turkey to acquiesce, due to their lack of territorial continuity with it, but not the easiest for Greece to acquire admittedly. Then again, even a neutral rump state like the e.g. Free City of Danzig would propably be closer to the Soviet interests to ensure free and unrestricted access to the Bosporus channel at the very least, than agreeing leave it to Turkey, because if a civil war takes place in the future, which is a very likely scenario, especially if the Soviets want to cement their influence over Turkey, then not only it would be a lost cause, they could never hope to occupy it, being completely cut off from Turkey as it is, and on top of that it would serve as a impregnable permanent base for the enemy western aligned Turkish side, which even though it would be dwarfed if the Turkish soviet aligned side wins the civil war, it would sorta be like an ATL ROC/Taiwan like state, denying the legitimacy of the Turkish state, acting as a constant thorn to the Soviet efforts there.
The Greeks would likely have a fair chance to win a plebiscite on the European side. Of course again great power politics make things interesting...
The area was often considered together with Dodecanese and the Greeks are getting Dodecanese. They likely have a good propaganda claim on at least part of Caria what with Miletus and Halicarnassus being there and only Turkey would be caring... unless someone points the Soviets to Marmaris and the former Italian naval base there, modern Aksaz?
Rhodes is the one thing the Greeks are getting for certain "blessed the holding the land" and all that.
One problem is... what communist faction? The Turkish communist party was pretty much on the fringes of society...
As for the communist faction, propably shouldn't had call it that, more likely it is a Kemalist/leftist/secularist faction that is aligned with the Soviets, fighting out against a Islamist-Conservative faction, maybe with a sizable wing that favors the restoration of the Ottoman Sultan, after all the Kemalists have brought about x5 the territorial losses that the old Sultan was deposed for, in '23 and '45 again they could claim. That's more alike to the Turkish political landscape.
That being said, if the Kemalist side survives at the very least a future civil war, whether Turkey is divided or united post civil war, I could see the ruling ITTL Kemalist party being severely influenced by the Soviet Union, after being brought in its sphere of influence, (the ITTL version of the Warsaw Pact), just like their IRL counterparts in the GDR. Given time, some decades to be precise, that would swift the ITTL Kemalist party's ideology to be more akin to the Marxist-Leninist orthodoxy (as in dogmatically speaking, not religious wise).