Poland and the Baltic states are supporting Ukraine in order to keep the Russians pushed back. I think they rightly assess Putin won't survive a military defeat in Ukraine, so they're doing what they can to assure his destruction, ideally without starting WWIII.
But fighting a proxy war (and I agree with that part of your premise) is a VERY different prospect than taking NATO head-on. You fight a proxy war to fight the war you wouldn't fight directly. So, in a world of escalations, that would be a doozy, with a strong chance of nuclear involvement. Based on what I've seen in the public domain, Russia hasn't increased it's conscription rate, so it doesn't yet appear Putin is undergoing a major military buildup for a follow-on campaign. If anything, his military is weaker than before, and now the world knows it. So the loss-of-face and wounded beast arguments, I can understand. But even if Putin gains territory in Ukraine out of this, I don't believe he'd risk his own existence on the Baltics or Poland.
My prediction right now is that this will drag on for some time, at great cost to Ukraine, and resource distribution (mainly food and fuel) in Europe and Asia will suffer. Russia will eventually gain territory in Eastern Ukraine, but at a high price, and be done militarily for a while as they lick their wounds and try to salvage what's left of their economy. Putin will remain in power until he dies, and resume his not-so-shadowy game of discrediting the West and supplying our enemies at every opportunity.
All based on what (I think) is known today. If Putin, or the West, get even more irrational, all my bets are off.