My takeaway is that Russia, China's vassal, wanted to use nukes and China told them they can't[1].
I don't believe Russia really cares about the rest of the planet. At the same time, China doesn't care if Russia gets a bloody nose on Putin's little vanity project and realizes a nuclear war is bad for their mercantile economy.
[1] https://www.politico.eu/article/volodymyr-zelenskyy-china-ur...
This coming from the leader of the other country in a war... I mean, I do find it credible that Xi might have told Putin to think very hard before doing something extremely stupid, but from there to stating that Russia is "China's vassal" and will do whatever they're told by a party who has long been a direct competitor (China and Russia have been solid "frenemies" for a long time, pushing very different views of what "real socialism" looks like)... It's a big jump.
The Soviet Union's relationship with China was more of a peer rivalry situation. The Russian relationship with China is nowhere near parity. Russia would fold tomorrow if China withdrew their backing and went along with the US/EU sanctions.
So Russia is only able to prosecute their war with China's permission. When your foreign policy is decided by another power, that's the textbook definition of a vassal.