"Technological and societal evolution has now reached a level of complexity that
renders the probability of human survival for the next 1,000 years drastically
higher than at any previous stage of our long history."

I agree, if the question is biological survivial. It's possible for humans to biologically survive even if we were hit by a extinction level impactor. Biologically humans have a better chance than the cockroaches- despite the common claim about the cockroaches superior chances.

But Earth is evenually a death trap. So the question is will humans survive that also have the potential for space travel. That's a different question.
The other question is will human living in space survive better than say the fate of the colony on Easter Island.
If living space is NOT something requiring inhabitants on Earth to continually subsidize the activity and is actually prosperous- perhaps far more prosperous than living anywhere on Earth, that make space development worthwhile.
If Space is not environment in which humans can thrive, then it wouldn't be worth the bother- something done for amusement perhaps but not significant.