Plus a bit of evolution for that coral, I'm guessing. Nature will eventually adapt to whatever we throw at it, but I'm not so sure if it will be fast enough for humans to survive.
Not true in the slightest; evolution is solely driven by differential reproduction rates. You'll see evolutionary dynamics even if every organism you study is immortal and invulnerable.
Dying is just one of many things that affect your ability to reproduce.
Are rich countries like US/EU etc. going to just allow tens/hundreds of millions of Africans to immigrate into their country when large parts of their continent become uninhabitable ?
Or are we going to quietly just let them die like is happening now.
If they could manage the sort of wealth generation seen in China or India, they probably could make it through any amount of climate change due to having lots of cheap energy.