It’s also conceivable that Putin will take a gamble on Ukraine and move in if China chooses to act.

I think Putin is wiser than that. That risks escalating into a world war. In a general state of war, it could drag the EU into a war with Russia as well. Putin is a very cautious man and I think he'll wait out a sino-American war. Both sides will be weaker at the end of it, regardless of the victor. If it leads to a nuclear exchange, they'd be even weaker, giving Russia a much stronger hand in the post-war world.

He'd prefer that China win and throughout the war, he'll sell gas, oil, raw materials, food and arms to China. The US would not like it, but wouldn't do anything about it as an attack on Russian infrastructure is tantamount to a declaration of war on Russia and Russia arguably has the strongest nuclear arsenal in the world.

Russia would get fat from all the money they'd make from oil, gas, arms, and grain sale, and it would be more powerful on the world stage at the conclusion of the war. The same goes for the EU. Their manufacturing would make a killing in absence of China on the world stage.