EU should think really hard over if they want to be a party to American aggression over Taiwan.
If rest of NATO not only doesn't declare opposition to US annexation but aids them in any form, they're party to the conflict.
America seems to assume China will only fight on sea where US has numbers advantage, and they have built up Japan, Guam, Tindal, possibly the Philippines as America's island chain.
Why would China not go around America's maginot line and hit Europe directly together with the Russian federation?
America has around 100k troops in Europe. Most of the European forces are demilitarised. Ukraine has a bunch of stuff owing to massive soviet stockpiles, besides that, only France and Poland have some degree of major standing military. Turkey has a force that could be on par with Ukraine, but its doubtful they will give their all to defend Northern Europe.
Non US NATO are just colonial police units that exist to lend credibility to US when America invades others and does the actual hard work. They're the soft underbelly, and China should not miss its chance to gut them.
What arms would China supply Russia that would allow it to end the war quickly though?
I can only think of ISR and drones, but even then, still not likely to suddenly make the war end quickly in Russia's favor.
Firstly, just by instructing Putin that it is time to let Ukrainian leadership die.
DF series missiles and stealth drones to make sure that actually happens (even if Russians should have their own means), backed by satellite data and ISR drones.
Next, a lot of rocket artillery and strike drones.
Short of actually putting boots on the ground, there wouldn't be the 1 month rout effect like in the Korean war, but maybe 3-4 months to make Ukraine completely unlivable while their soldiers have no command left.