China wants a new world order where they are masters. They also see the lessons of the 20th century clearly. That is it is far better to be the worlds hegemonic master than to try to conquer and rule it in the traditional sense. Exactly non of this is possible though unless their sphere of influence appears irresistible. To that end they can't have a island they claim to rule sitting there doing its own thing, and worse being nominally oriented to the existing global power structure.
They also rightly see the rather 19th century western model of national borders being determined by a few world powers who make agreements about lines on map without regard to the reality on the ground or blood sacrifices the plebs for the political theater of the occasional proxy-'fight' over those borders, as limiting.
China wants to be able to use both soft power and hard power whichever seems least costly / most expeditious and have the results stick. To that end they have seen the muted response to Russia's actions in Ukraine as useful.
However the reality is Ukraine is not part of NATO, Europe is weal and broke, the USA is strong but broke, and nobody wants to see the mass destruction that would result from a atomic contest with Russia. So a truly muscular defense of Ukraine was never going to happen, is never going to happen. The mistake politically was not ignoring the situation. In making a fuss over it we have turned it into the precedent setting event China wants if Russia succeeds.
Ironically as far as US political influence is concerned, thwarting Russia is becoming important in a way it never needed be and wasn't four years ago. We made to big deal about it, so now we have to show we have influence and the ability to impose our vision. What we should of done is handled it like Crimea, looked the other way and it would have been no big deal in geo-politics or US power. Now we have to both avoid a hot contest with Putin AND win proxy-war. We are not that good at proxy-wars... Biden and Blinken really FUCKED UP.