I don't see why or how the step 3 would happen. Even if NK nuked South Korea, and even if theoretically US responded with a nuclear strike(and that is already really stretching it), why would other superpowers respond with their own nuclear strikes? China would be super unhappy, sure, but would they attack US with nukes over destruction of North Korea? I don't see it.
I can see Pakistan and India exchanging nukes, but why would anyone join in that?
NK nukes SK, USA nukes NK, CCP needs to show that they are not weak and nukes something America-adjacent (ex: Guam). I think all bets are off at that point.
There is a contingent of generals in every nuclear capable country which is itching to use them. Historically, it has only been a rational civilian leader who has kept them in check.
There was recently a US President who was talking about nuking a hurricane.[0] Once nuclear weapons are in play, we just need one irrational reactionary leader, in the wrong place, at the wrong time, and Fin.
1) A surprise meteor hits Pyongyang or Islamabad.
2) Their military hits their preprogrammed nuclear targets.
3) This draws larger powers into a nuclear exchange.
4) Fin.
But really, I think a bioweapon made by some kid in >2070 is probably more likely.