I think there is very little risk of a nuclear war sparked by the proxy war in Ukraine. That's because there is now no hope of NATO winning and so no need for Russia to start using its tactical nuclear weapons in Ukraine, which would have carried a greater risk of mistakes being made and nuclear escalation occurring.
Regarding American military and economic power, I see no reason to believe it's crumbling. American world hegemony, in my view, ended around 2017 with China establishing herself as a peer competitor.
However the US is still the world's only regional hegemon and still has the most powerful combination of military and economic power in the world. That of course could change with China becoming more powerful. So America is determined to prevent China from ever becoming a regional hegemon in Asia.
Therefore, in my view, a nuclear WWIII between the US and China is MUCH less unlikely than one between NATO and Russia..
