Treaty of Sèvres: How does WW2 look?

Lets assume that everything goes wrong for the Turks after WW1, and they ultimately have to accept the Treaty of Sèvres more or less exactly as the Allies intended. When the dust settles:
- Greece has Smyrna, more of East Thrace, and, de facto, the Zone of the Straits and Constantinople, though those remain formally an international zone until a plebiscite at some point in the late 20s, early 30s formally puts them in Greece. Greece does not try to push further into Anatolia than that - with the eventual incorporation of the Zone of the Straits, their territory is pretty much contiguous.
- Wilsonian Armenia survives.
- Kurdistan comes into existence, and eventually, the French give them Hatay, so they have a port.
- The zones of influence of the victorious but war-weary Allies are gradually abandoned over the 20s, to consolidate their holds on their new mandates and colonies.

So, Turkey is still mostly there, but definitely trimmed back compared to its historical borders. How does this impact WW2 (assume it occurs more or less on schedule)? It may seem that Turkey would almost certainly join the Axis, but I don't think that should be taken for granted. They lost a lot in WW1 and that wasn't enough to encourage a revanchist spirit, historically. Perhaps Greece holds out longer, with resources across the Aegean from any Axis lines of attack (unless Turkey joins the Axis, of course). If Turkey does join the Axis, I expect to see them attack Armenia and Kurdistan, as well.

Beyond that, what else might change? I don't think, even if Turkey joins the Axis, this is enough to change the ultimate outcome of WW2. As a nation, they've already been trimmed back to pretty much the bare minimum borders, without some serious ethnic cleansing (which likely already happened by this point anyway).

Or if they don't join the Axis, how does that impact the ultimate outcome of the war, especially if this larger Greece is able to be a thorn in the Axis side for longer? Ironically, that might actually be a blessing in disguise, if Greece distracts Hitler long enough, he might have to delay Barbarossa even longer, and wait until the next spring. By which point, the US might be in the war, and his generals convince him to focus on the west. What Stalin does in that scenario is anyone's guess. Maybe he just watches the Capitalists and Fascists club each other, maybe he stabs Hitler in the back, maybe they do the unthinkable and solidify the M-R pact into a formal alliance? Probably option 1, in my opinion, until Germany is really on the ropes, and then the Red Army comes in to liberate Eastern Europe.
 
Does the Greek-Turkish war 1919-1922 still take place?
Does the Turkish National Movement still happen?
 
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