Nuclear war would do serious economic damage. We'd target ports and refineries, so involved countries would mostly halt trading.

Nuclear war would not bring long lasting radiation like nuclear power plant meltdowns do:

"An estimated 60 percent of the deaths were from burns, 30 percent from the blast, and 10 percent from radiation."

"Although some scientists expected that Hiroshima and Nagasaki would be uninhabitable for generations because of the radiation caused by the atomic weapons, in reality radiation in the cities had returned to near normal one month after the bombings."

Also nuclear winter was always grossly exaggerated.

The pessimistic nuclear winter model starts from roughly Owen Toon estimate of acreage burned from megatonnes, after which one assumes some atmospheric conditions and argues what the hot soot does.

In 2023, the Canadian wildfires alone burned enough acreage that if you run this estimate backwards, then the fires resembled a nuclear war of 2000 megatonnes. It darkened the skies above NYC for several weeks, so really quite major, but not crop failures.

We do not have 2000 megatonnes of warheads deployed, because of treaties, and because warheads got smaller as missiles became more accurate. Afaik nuclear winter seems impossible with current stockpiles. China building more bombs shall not change this picture.

I've never checked if nuclear summer maybe real, but James Anderson says climate change shall cause similar ozone degradation anyways.

Nuclear war would directly effect people who live near relevant infrastructure in the involved countries, with ports and bases being the major concerns. It'd effect others primarily through trade disruptions

In brief, climate change should scare you far more than nuclear war:

IPCC predicts +3°C by 2100, but +4°C should mean uninhabitable tropics and world carrying capacity below 1 billion humans. See page 37 of The Nature of the Challenge or 36m in Will Steffen's 2018 talk), or Steve Keen on Nordhaus et al

If otoh you lead a nation then clearly you should make choices that keep your nation out of nuclear wars. It'll likely be oil deependence that causes nuclear war though. We should increase fuel taxes, expand production of renewables, and expand electrification, so that we can keep out of whatever conflicts do turn into nuclear wars.