I live close to the site of the Marshall fire in Colorado which destroyed a thousand homes at the end of 2021. The amount of soot was surprisingly large. After post-fire snowfalls, snow pushed to the edges of parking lots was blacker than usual, probably from soot already on the ground that got scraped up with the snow. The other day I saw a couple of workers shovel soot off the Costco roof into a truck. In addition to more soot than I expected, it was more toxic (according to local reports) from all the plastics and chemicals that were burned.

Did WWII blacken the planet with soot from firebombing? The bombing of Tokyo alone was 1.6 megatons of bombs, for example.

I honestly have no idea, and perhaps our sensors were not accurate enough at the time.

My guess, based on little other than a gut feel, is that while a lot of explosives were dropped on Tokyo, the energy was not concentrated enough to lift the soot high enough to be a global problem. But also, 1.6Mt just isn't that big a blast if you're talking nukes. Yes, it's bigger than current individual service warheads, but not by all that much. The B83 goes up to 1.2Mt.

To put another bound on the question, Krakatoa was estimated at 200Mt in a single blast, and that definitely did affect the global climate. Again gut feel, but my suspicion would be that many distributed explosions around the globe totalling 200Mt would be worse in terms of direct effect just because there would be more physical mass available to be thrown into the air. Plus the soot would be radioactive.