That's no what the IPCC reports say. Even under the pessimistic scenarios, we're on track for "billions of humans die", not "earth becomes literally unlivable" (though some of it depends on how bad some feedback loops are).
Under the "countries respect their current pledges" scenario, we're heading for 2.8°C of warming, which is "floods and heatwaves everywhere, billions of refugees" level, not remotely close to extinction.
Worse, the massive AI spending and energy use is making said environmental catastrophe happen faster.
The invention of contraception did more damage to human population than all of the environmental damage combined, projected forward to 2100, and then multiplied by 10.
Humans are hilariously resistant to environmental changes. Humans simply adapt too fast for the environment to catch them.
What makes AI a credible threat is that AI is intelligent. AI could play the same adaptation game humanity does - and win.