Nuclear war would be absolutely apocalyptic. Lookup the US policy on “Launch on Warning” and “Hair-trigger alert”. Russia has the same thing and China by this point probably does, too. If the US were targeted those doctrines would come into effect and we’d go into “escalate to de-escalate” mode. And that’d make it worse.

There would be multiple thousands of warheads launched around the globe. EMPs would be detonated in the atmosphere, continent-wide power grids would fail. A single Ohio-class nuclear submarine has more destructive power than every bomb, including the two nukes, dropped in WWII — and they’d light the place up. And then you have all the various contamination in the air, soil, and water that would be cycled through the ecosystem for hundreds and thousands of years.

Pockets of people would live, certainly, but it’d be awful. Like Khrushchev said, “the survivors will envy the dead.”