On one hand many countries will invest in heavy industry, manufacturing, and fall back to fossil fuels.
On the other hand, economy overall should slow down and consumption of non-essential goods and services will drop.
I’m not expecting any definite answers or numbers, of course, just some food for thought.
The tools that would kill enough humans to matter would hurt the biosphere much worse than it hurts humans. Otters and bees don’t have gas masks and nuclear shelters.