Nukes won’t destroy the planet. All their yields combined don’t measure up to a 1 km asteroid or an average supervolcano, and their radiation and dust is gone in 0.00005% of the remaining time Earth will exist.

The chemical pollution of all our industry washing out to sea will have a bigger impact. All ocean-based animals with shells will die out as oceanic acidity reaches critical levels, though in 0.01% of the remaining time earth will exist shell-based life from freshwater habitats would probablu repopulate them if non-shell-based life doesn’t evolve to fill the same niches first.

There will be trees, flowers, mammals, shellfish, algae, fungi, birds, reptiles, and insects. The Earth from above will look like ocean, forest, desert, and glacier, though the forests may cover less of it for the first 0.01% of the remainder of its existence. We will produce a mass extinction event comparable to the other five, but Earth will still look the same at the scale of a simple drawing.

If you blow up all our nukes in the same place at once, you will make a bill hole and a hell lotta dust, but you certainly won’t destroy the planet or kill all life. In that case you might dessimate a lot of large animal and plant species. But there would still be survivors, probably including humans. Their lives would probably be miserable for a long time too. But anyway, we’re talking about climate change, not nukes, so I don’t get why you’re bringing that up?