Overshooting your carrying capacity as a species rarely leads to extinction. It leads to population crashes, for sure. If we don't limit our own growth, no doubt we will enter a bottleneck period. Good chance we're at the very start of one now, just most people can't see it yet.

With population booms and busts, it will become harder and harder to maintain any kind of meaningful civilization, so with that bottleneck will most likely come collapse.

But that's not extinction.

That said, running headlong into a bottleneck while simultaneously having to face a period of adaptation (hotter world) and losing your energy source in an age where running out of enough skilled people to handle certain things that have already been set I to motion (nuclear energy and weapons) that would otherwise decimate and pollute the world does not bode well for team human. And also, we're also at the start of a mass extinction event, which usually takes out speciesnat the top of the food chain. That's includes us, if anyone is confused.