What makes you think this? Even in the worst case scenarios, I can imagine a smaller global population surviving in what remains.
>smaller global population surviving
This is just an unfound assumption on your part. Passenger pigeons went from billions of birds to extinct in less than a century. There are hundreds of different scenarios around climate change and disease evolution alone that could wipe us pretty quickly and a rapidly falling population would make it worse quickly as things like new medicines could not be developed quickly enough, or more technology couldn't be created fast enough (unless we have full AGI working on itself, but then you have alignment being its own problem).
I simply find it unlikely that any amount of climate change (beyond the eventual death of our sun) will result in the complete elimination of humanity.
Yes, there are many likely bad scenarios that would drastically reduce the population.
What sort of non-climate-threat do you suppose will take us out?