Humanity will adapt and overcome even if there is such a great warming (which may not happen due to geoengineering). We have survived far more serious threats (e.g. Toba, Ice Age) with far less technology.
Think about what you just said there, Jakob.
Humanity survived Toba, an ice age, and probably many other disasters we're aware of.
Human civilization, however, was never put under such stresses. Whenever it was tested in lesser ways, it tended to break down very quickly. The worst we experienced was a little "ice age" and a year without a summer, the former of which pushed humankind to the limit (our worst period as a species since the rise of civilization was between 1200 and 1400). Meanwhile, older civilizations collapsed and vanished due to climatic changes or abrupt disasters, and later ones have been put through the wringer and only survived due to a more globalized world. Imagine if the rest of the world can't come to the aid of a nation in the middle of total social meltdown because the same thing is happening everywhere. Civilization won't survive, even if humans do.
You know how I keep heralding AGI as our great (and only possible) savior? Because the key towards rebuilding (or building) anything is knowledge + capability + resources. Right know, knowledge is very fragile and there are no singular human beings who would know absolutely everything necessary to jumpstart a new neo-modern civilization in the immediate aftermath of a disaster. And even if there were, the human population would be too greatly reduced to make it feasible. Most humans alive after a nuclear war, for example, would be impoverished farmers in the global South, so we'd be living in a world where nations like Peru, Zimbabwe, and New Zealand are global superpowers. Hence why I go all in on machine lords and supercapable technotarians, independent of humans. When we have that, we can start to ease our worries about surviving existential threats that even destroy civilization because rebuilding would take so little effort as long as we have access to resources. In our case, we can't return to fossil fuels after the 21st century even if we wanted to. Any future civilization that arises after the collapse of this would is stuck going from burning wood and whale oil straight to nuclear fission and wind power.
I'd rather not lose civilization in the first place.