I don't subscribe to the NYT and there is a paywall on the link but the situation is always more complex than portrayed.
Russia will not directly support Assad against Turkey but will support Assad as the "legitimate" [Putin's words] government of Syria.
Putin is saying that he seeks a solution between Syrians at a negotiating table (I've been saying the same for years) and that all uninvited forces should leave (that includes Turkey).
Putin knows that Turkey won't leave but maybe hoping for a limitation on the Turkish offensive.
I note just a snippet of criticism from Putin towards the Assad Government being responsible for what has happened over the last decade. I interpret this along with what else Putin is saying as an intent to pressurise Assad into a more conciliatory mindset. Assad's mindset needs to be more open for discussion IMHO and my suspicion is that Putin is pushing in that direction.
Moving off what Putin has been saying today, there is a Foreign Policy article that points quite well to the failures of US policy (short sightedness and lack of a roadmap) and which clearly outlines Turkey's longer term goal which has always been to change the ethic composition of North Syria.
Back to Putin, he is highlighting the return of Syrians to Government controlled areas because they trust the guarantees thus provided. Overlaying the Turkish agenda, I again see Putin pushing Assad to be inclusive in the north of the country. Putin does not (purposely) mention the word Kurds however I see him pushing Assad to include them in the Constitutional Committee.
Putin says he is not the mediator for the ME but he is. He is correct in saying there are no rewards for the mediator however with reasonable relations with all the major ME players that is where he sits. In truth Russia has no alternative other than to play honest broker for once.
Back to the SDF. IMO Assad needs the largely Sunni Kurds to maintain something of a peace with conservative Sunni Arab tribes who at this point in time distrust the Assad Regime. The Kurds similarly need Assad and will instantly need to rebadge themselves if the situation is to be controlled. From that point Assad could argue that there is only one Syrian Army and that the YPG (that Turkey says it is fighting) does not exist. But again, Assad needs to retain the civil structures in the north to keep the population there on side with a national agenda ……. that will start with a round table, coffee and some further constitutional drafts.
