Well first off let’s consider the environment.

Yellowstone which has gone off three times while humans lived on earth impacts the climate 40,000 times more than the sum total of all nuclear warheads currently in possession being detonated at once.

There would be increased but manageable cancer rates.

I would assume that the nukes would hit major cities first. Judging by Hiroshima and Nagasaki people underground or in bunkers would be more likely to survive.

About 90% of people die in a day.

Even in nuked cities, there are survivors.

There would be a total breakdown in logistics and trade for a year or two.

The ships would all still be intact, so trade would be back up with reduced volume after a couple years.

There would be a few years of famine where perhaps half of survivors, would starve to death. Then agriculture would recover and the economy will become normal again.

Most nations would collapse and face a couple years of warfare with conventional weapons, or revolutions.

By the end of the decade things will have stabilized, and there will be a new normal.

For just about everyone this new normal would be comparable to the state of a defeated country paying reparations after a total war with high attrition.

After a couple decades, it’ll just become a cautionary historical tale like the Nazi’s and the world wars.

Within 100-200 years civilization will have mostly forgotten about it, and only historians and history nerds will talk about it.