There is the alternate option...during the meeting on 14th Biden will give Turkey the opportunity to buy the oil directly here and be the only buyer, creating another Barzani statelet that Turkey will accept.
In return, Turkey will annex the areas it has occupied such as Idlib. I do not think it is a great deal. Idlib will be a huge problem in future. We would be absorbing a massive population, some of which are absolutely radical. But rumours say Turkey is currently building a governor's office in Idlib.
For Erdogan to survive, US support would help him a lot. Perhaps annexation of land is something that will as well, bringing the ummah together or whatever.
Indicator will be yarubiye gate.
Russia also think Turkey will annex:
Syrian army shelling is more frequent and deeper parts of Idlib are being targetted.