Maybe Putin's non-invocation (up to now) of the nuclear umbrella shows he is as eager as anyone to maintain it as the ultimate protection against existential threats. The US's sharp turn away from globalism is a gift to Putin, and, given that the US population is strongly divided over the changes the current administration is making, that might be threatened if Russia were to act more belligerently than it already is.
Personally, I'm more concerned over what will happen if and when the situation becomes one in which Trump realizes he's going to be seen as the president who 'lost' Taiwan.
The US is claiming 700,000+ Russian killed and wounded so far. Moscow obviously think something here is a threat to the long term integrity and security of Russia. That is serious commitment.
Unless the US is lying. I hope they are, to be honest. Mountains of skulls are fun in D&D but not in real wars.
I share your feelings about the entirely avoidable horror of it all.
So if a land invasion by foreign troops is going to be interpreted as no big deal, why would the fall of Poland matter from a nuclear standpoint? You can see it building in the public discourse as people convince themselves that they can push to an absurd distance without Russia being able to respond - we've seen their border integrity violated, strikes on Moscow, British missiles being lobbed in to Russian territories, an explicit US strategy of bleeding them out and fairly credible calls for regime change where it isn't obvious how far the US is acting on the idea.
If we assume by symmetry that the US would take similar abuse before it launched any nukes, what on earth is supposed to happen in Europe to provoke a serious response? I wouldn't chance it, but it looks a lot like they're bluffing a willingness to do anything and some idiot dressed up as a general will one day will do something really stupid. We're exploring for the line where Russia breaks the nuclear taboo here; as far as I remember the game-theoretic response to salami tactics is supposed to be wildly disproportionate aggression. And there is a decent chance that it'll go unpunished since the US is clearly not going to stand up for Ukraine to the point where it risks blowback to the US proper.