A general nuclear exchange would be the end of civilization as we know it. Possibly worse than that in the longer term.
The US is incapable of stopping a Russian nuclear volley. It is possible that the US could take down a few weapons. But the Russians have the number available to easily overwhelm US defenses. The same goes the other way around. Russia has some very sophisticated air defense, especially around Moscow. But they would be overwhelmed by any US response.
Now I could see the current conflict in Ukraine resulting in some tactical nuclear exchange (but hope not). The Russians have a large advantage in numbers of tactical nukes. And Putin seems capable of such a thing. His Iskander medium range missiles are capable of hitting most military targets in Europe, and are both hypersonic and claimed to have a maneuvering warhead. Not likely that they can be intercepted with any surety. (Note also that many nuclear weapons systems have what is called, salvage fusing. They are designed to detonate even if they are hit.)
Putin has been preparing Russia's military with asymmetric capabilities to make up for the difference in defense budgets between Russia and the West.
In 10 minutes Putin could render Western Europe mostly devoid of any serious military capability, so that they would be incapable of threatening Russia for a long time to come. The question would be, how would the US (and Britain & France) respond. Any US response against the Russian homeland would also mean serious destruction in the continental US. In such a tactical strike on Western Europe, Russia might even leave Britain and France alone to let them think about their future.
I hope all this ends up being no more than theoretical chit-chat. But it appears that the world is already changed significantly in the last few days. What was a world economy has suddenly become two entrenched camps, East vs. West. And both sides appear to be feeling capable of sticking with their own viewpoint. This situation has been building for awhile. But we have now reached a new level of entrenchment. It's hard to see how things could return to the 'normal' we used to live with.