I have never heard of extinction as a possible consequence of climate change. Care to elaborate how that might be possible? Even if society crumbles due to unrest, the Earth will be inhabitable in at least some areas. It's hard to imagine that every single human being on Earth will die.
There have already been multiple mass extinctions in the past driven by global climate shift. There are currently 1 million species at risk of extinction right now, which is a significant fraction of known species. Full on ecological collapse has been happening on all fronts for years, and it still continues to accelerate. "society" isnt responsible for pollinating plants or turning co2 into o2, and it's scary how easily and completely people forget that in just one generation. There is alot of middle ground between billions of humans and thousands of humans, and i think its safe to say if and when we are reduced to thousands that the rest of the planet will be destroyed beyond any hope of recovery.
Maybe most agriculture will have to happen indoors? Chile, Spain and many other year-round producers do it in greenhouses / hoop tunnels. Vertical farming/airoponics and so on to help scale food production.
I think the bigger problem is if we kill the ocean through sea level rise, warming, deoxygenation and acidification, then we kill 3/4 of oxygen production (but we would still have 100k-400k years supply) and 2%+ of the food supply.
Maybe my wording conflates unintentionally meaning "extinction of humans" with "extinctions of many species." Extinction of many species is happening at several orders-of-magnitude of background, historical trends. Homo sapiens sapiens extinction outright is unlikely unless we double-down on emissions.
Let's call climate change a "Dial-a-yield" planetary nuke that will extinct many species and most likely reduce our numbers anywhere from 1-50 million if nothing is done, e.g., pre-historic levels. We have to make drastic changes now to dial back the "yield." How bad climate change has to be is ultimately up to all people across the world, here and now.