The World War to Save Livable Ecology.

Nuclear war would probably be a net benefit to ecology of earth as the fallout half-life of modern nuclear weapons is short. Also, many animals and plants are more resilient in important ways than are humans, and the biodeversity near cities that would be obliterated is far lower than forest/wilderness areas that would be relatively unscathed.

Full-scale nuclear exchange would cause humans to go extinct or nearly so, but would probably not directly cause that many more animal/plant extinctions for various reasons, some of which are mentioned above.

Also, “nuclear winter” is probably a myth as modern nuclear weapons are almost all air-bursted. (And because the burning of the Kuwaiti oil fields during the first Gulf War caused a scientific re-thinking of the effects of even very large fires on the atmosphere.)

Net result of nuclear war is that in 200 years, the biosphere would be well on the way to recovery.