FWIW, the only way nuclear weapons wipe out all of humanity is if they start unprecedentedly large fires that change the climate.
At peak, we had about 80k nukes (way less now). That’s nowhere near enough to kill all 8bn people (as spread out as we are).
The way nukes end humanity is blacking out the sun and reducing plant/food output.
Directly? Probably not. But the contamination from fallout is more than sufficient to poison a significant fraction of humans over a not-too-long time horizon and provide everybody else with a significant cancer risk. The ensuing chaos and resulting breakdown of civilization will do the rest. Don't believe it? Ever seen the panic when toilet paper is at risk to run out at Walmart?
Those who still remember the Chernobyl disaster are aware what that meant for Europe. A single plant, and everybody got warned and could take precautions.
There’s just not that much nuclear material in a given bomb (and the whole point is to release as much energy as possible as quickly as possible), whereas Chernobyl is dangerous because the elephants foot is gigantic and still uranium.
Now combine that with nuclear winter and resulting consequences for crops and lifestock. We don't all need to die directly from bombs. Just a minor disruption in stability and hunger and civil unrest do the rest.
[1] It's pretty fascinating how vulnerable our societies are. Other results are things like .. 3 days power outage and you'd also be on the verge of civil war if government doesn't immediately pour in enormous resources in crisis management.