I normally call what's happening 'global warming' or 'climate catastrophe.'
I've had no truck with 'climate change.' It was always obviously a fudge.
We're not yet in a major extinction - remember that in the Permian Great Dying 95% of animals and plants on earth and in the seas... well... died. The Earth recovered in only 20 million years.
Let's look this squarely in the face: what we are actually facing in not 'extinction' but 'human extinction.'
As in our species of fire-apes, water-apes, dropping from 8 billion to 4 billion to 2 billion to 1 billion to half a billion extremely rapidly.
Using those old favourite equestrians Famine, Plague, War and Death.
Obviously everyone will suffer immensely before they die. Perhaps a few billionaires will survive in their fortresses in New Zealand and die of old age, but most people won't.
Once we're all gone, the Earth will recover and depending how many residual species we leave, it may take only a million years or two before she starts evolving new species to take the places of those that died.
I don't think she'll experiment with primates again, though.