The US were determined to stop the rise of the PRC. The US remembered 1951, when General MacArthur told President Truman that the only way the US could defeat the PLA was to use nukes. President Truman said, 'The USSR has MAD. You're fired!'
The US are again determined to stop the rise of the PRC. It's been called the Thucydides Trap for the last 8 or so years. Every hegemon, historically beginning with Sparta in ancient Greece, does all it can to prevent a rising rival from overtaking it and becoming the new hegemon (probably happened many times before, but did not make the history books since history books hadn't been around all that long when Sparta was hegemon).
And today the US hegemon are worried about the rise of the PRC, but, based on what happened in 1951, figured it would be best to first break up Russia into several smaller, unarmed states that always had to do whatever the US said, so the US prepared to make the Ukraine part of NATO and put in nukes and ABMs to eliminate Russian MAD, after which Russia would have to do whatever the US ordered, and would have to split into those small, unarmed countries. Then, with no Russia, the PRC would be next. The US and NATO both wrote to Russia that this was going to happen and there was nothing Russia could do about it.
This is working out very well in the Western establishment media. The Ukrainians with their advanced US weapons are easily defeating the Russians with their "outmoded and inept weapons" as the New York Times, CNN, et al. iterate daily. The Russians are proving an easier challenge than Grenada, Panama, Iraq, Yugoslavia, and Libya.
Sadly, reporters actually in the Donbass report that the Russians are winning. The 2014 coup in the Ukraine replaced a rabidly pro-Russian government that let everyone speak whatever language they liked and attend whatever church they liked with a strictly neutral government that banned everything Russian throughout the Ukraine and started killing people who spoke Russian or tried to attend a Russian Orthodox Church. Russia forced the Ukraine to sign the Minsk agreement promising to leave the Russians alone, and the Ukraine and US used the next 8 years building impregnable fortresses: so much steel and concrete that no bomb, no artillery can penetrate, but with doors that open and allow artillery strikes when the Russians aren't bombing or shelling. So Russian progress against these fortresses has been very slow but steady. One by one, the fortress defenders run out of food and water and have to either surrender or try to retreat while the Russian Air Force and artillery and mobile armour try to kill as many as possible.
But it is illegal to write anything in the West except that the Ukrainians with US weapons are destroying the Russians, they have destroyed every Russian tank and aircraft, the Russians cannot and do not face the Ukrainian military, they only shell undefended cities and villages killing only civilians. So things are going very, very well, and the small sacrifices the US, Canada, and European citizens must make to preserve democracy--i.e., not enough food, electricity, heat, or petrol--won't be necessary for much longer, and anyone can put up with cold showers for a few weeks if it means saving Democracy.
But now, Speaker Pelosi wants to visit Taiwan, and the PRC say such a visit will necessitate a military response, so the entire Senate, Democrat and Republican, say she must go to show the PRC they cannot challenge the US and get away with it. The US military and White House have all begged her not to go, but it's not at all clear is she will listen. The Democrats are sure this will look very good for the upcoming election when Speaker Pelosi proves that the PRC are no match for a US Democrat Speaker.
So it looks like the US want a 2 Front proxy war where the Ukraine, with US weapons, will destroy Russia, and Taiwan, with US weapons, will destroy the PRC.
No one knows what would happen in a strictly conventional war with Russia against all of NATO. But everyone should know what will happen in a strictly conventional war with the PRC against all of NATO plus Japan and South Korea. Basically, in a week or so, NATO will no longer have any Air Force, Navy, or Army. And all with strictly conventional weapons.
So will NATO then nuke Russia and the PRC and end the entire world? After all, if there is no world, the US cannot be forced to see the PRC take over as world hegemon.