Does anyone have thoughts on the Venus Project? They have a very interesting suggested reading list. If you download their produced PDF on the project. It has some interesting language as well. It suggests, that they will build a new society after a nuclear WW3. It has a large number of people working on it for some time now.
https://www.thevenusproject.com/learn-more/recommended-books/
They theoretically can. Have had the increasing capability too for a long time. But it's a theory not a fact. There are protocols on the if. There are provisions to survive almost indefinitely providing the planet is secure.
However the problem becomes at what point does a nuclear war stop. And then at what cost to the planet. They're everywhere, some of the most remote locations, ice, islands, deserts, and some of the most built up, cities, and where they aren't are sooner equipping hunter killers, AI driven drones to search destroy and bunker bust, and dead man switches, and mobile launchers. Until they're becoming increasingly automated, launching, mobile launchers, drones, switches that once triggered release, and dead man switches. Automated almost to the point of their production. Look at these factories today. Into that future the robots are making robots. Why after technology has been virtually destroyed in any exchange do you want a less superior nation surviving with greater population numbers?
Eden project can theoretically repopulate the globe. I don't think it can terraform, rather in the correct conditions wait out radiation, and nuclear winter almost indefinitely. From there it can reseed the globe, almost every plant is archived and the seeds collected, it has the full genome database of every animal and can clone them. But it's all a pretty theory.
You meant destroy the planet, then evolve through it. Just to force a reset. Shiva. You'd have to be MAD. Hell, it will be back at it all over again. Next time. What have you solved?