There's a pretty substantial gap between "poor people starving" and "people with nukes care," but it's still plausible enough to be chilling, that's for sure.

The people with nukes would be the last to starve.

Also for anyone to go nuclear there would have to be a strategic goal for that Russia nuking the US won’t really help their food shortage and vice versa.

I agree but I think the chain can shorten to

nuclear war->there are maybe a few people left in bunkers.

If we were to get rid of the nuclear option then both your chain and my chain would not be viable.

Nukes before greenhouses?