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Once our climate reaches a new equilibrium, humanity will adjust and everything will probably be OK.Whatever remains of humanity will adjust and live the medieval or pre-medieval lives for the next many thousands of years.
The most fragile component of the climate change issue is human technological civilization. Once it breaks, it's game over. Most of us and most of our families won't make it. Current level of technology is maintained through a complex global supply chain involving millions of people. When that breaks, humanity will regress. Devices will die, there won't be a way to repair them. Survivors will regress maybe to early industrial era for a while, but since all easily accessible dense energy sources have already been used up, this won't last and the remnants of humanity will regress further, and stay there for God knows how long.
It's not a fate I'd wish on worst enemies.
As for how this collapse would happen? All the climate change-related "small" issues increasingly clogging our economy. More expensive food, more expensive water, less arable land, less habitable land, unprecedented migration. Eventually, there will be war. Or the global economy halts, and then there will be war.