One bone of contention is Russian air support to assist Syria in retaking territory, Idlib, that Turkey has occupied and used to shelter anti-Assad Islamist militias (not just them, but they're the real problem here--no militias, no need for much fighting, right?)

This repeats Idlib on a larger scale. Turkey occupying more Syrian territory and using Syrian refugees and Syrian militias to take and hold it to create a Turkish buffer zone while doing what Turks have done for 500+ years--work towards eradicating those pesky Kurds and create an ethnically superior, pure Turkish homeland for the relatively recent Turkish immigrants. (I mean, the Medes were immigrants at one point, too, the Hurrians and Urartu lost out).

I'm sure a clever manipulator could make this work to his favor--play off Turkey against Syria, make them work together at times but not *too* closely together--but it's like sticking your hand in a garbage disposal without turning off the power. You just hope nobody comes along and flips the wrong switch by accident. Russia's likely goal is probably more disruptive, with an eye to any Bosporus-based advantage it can get over NATO in military terms or, say, former Comecon countries like Bulgaria, Romania, and, ahem, Ukraine, in economic terms.

Mix in Iran. Iran's mostly pro-Syria, but has made nice to Turkey at times. Turkey's a better prize for Russia, but riskier than Syria. At the same time, while Russia and Iran are buddies, Iran's also had dealings with China. Russia and China are headed for problems that few like to talk about, and for now Putin's posturing to try to get China to think of Russia as an ally. Even used the word "alliance" buried in a public statement for where they're heading; to which China responded, buried in a similar kind of public statement, that it doesn't do alliances.

(Personally, I find that "China doesn't do alliances" to sum up and things nicely wrt China, and make some pretty clean-cut predictions.)