As far as I see it they would try for war in some form but they're also wary of taking direct conflicts.
No matter how US itself wants to spin it, China has escalation advantages in both Europe and Asia front. The only place they have higher initiative is South America.
Say whatever you want about Russian ineffeciency, culture of complacency etc. dragging out the war. 1 Russia alone that didn't use most of its own troops is still winning while the EU emptied its stockpiles into Ukraine and used all economical means.
Before the Ukraine war, it was believed that US had the escalation potential in Europe, but now the NATO economies and armies proved to be inflated.
If US overly invests into Europe front, China needs only to form a drone/ISR/artillery PVA that stays in the Russian rear to roll over the AFU no matter how much US tries to bolster it.
And some western copers think that China won't do this if it is advantageous to do, coping until the last that the Chinese government will do massive completely unforced errors and let the west fight Russia alone. The planners in Zhongnanhai are not stupid, the only scenario where Russia will be allowed to lose is if China could severely harvest Russia afterwards, where China judges that the increased control over Russia is worth temporarily reduced Russian power.
On the Asia front, if US wants to sling guns they can just invade Taiwan. The separatists are willing and ready. US isn't invading because doing so is too risky. There is only 1 possible way to invade Taiwan = full mobilisation and general draft. A SMO with 200 000 US troops and 2 CVBG will never cut it, trying so means a guaranteed humiliation and losing the rebel forces. But losing a war if US fully mobilized and drafted will mean the end of America as an unified country.
Therefore US is mainly trying to feel out what the borders are they can get away with without causing a direct war, because almost all war options are high risk and bad odds.
