What are our chances of survival for a long time?

[Anomalocaris]

Global warming and nuclear war won’t kill us all. It will just partially destroy organized civilization. It will put us behind a few hundred years, but we will rise again.

I suspect global warming or nuclear war won’t set us back So much as slow the progress of scientific and civilizational development hereon afterwards.

So after these events we will lag increasingly far behind compared to where would have been without them.   The period of decelerated development afterwards might last many decades to centuries before our progress resume their normal rate.   The deficit caused by the stagnation will probably remain and never be fully made up.