Putin is looking out for Russia's best interest. His past alliances were forged out of necessity. I don't see Russia holding Assad's hand right now as much as looking more cooperative to a valid US president, and his ability to make deals.
When Trump cut the Iran Deal out, EU scrambled to make energy deals with Russia. If that's the case, then what good is NATO in the end? EU was made an offer by Trump for energy. It was a deal they had to accept, else Trump would pull US support for NATO to a crawl. This, in turn, puts the US at an advantage in dealing with Russia moving forward. Putin is seeing new and better opportunities with Trump's administration. These opportunities are straightforward deals, chances at peace and deescalation of conflict in regions like Afghanistan, and cohesive efforts involving China in between.
With all the dirty deals with the EU, Russia, Iran, and China with US out of the picture, governments are going to be brought in line to more straightforward and fair trade. As long as everyone is cooperating, war will be off the docket for a while.
Deal making 101. If you have leverage, use it.