Yes, the 8 bln would will have to quickly come down with about 90% but this will not logically lead to human extinction.

There are quite a few forms of living in contexts that do not deplete the local environmental carrying capacities. Like fishing communities and nomands. And, like you mentioned, the crescent. Both the Chinees and the Mayan civilizations managed for thousands of years to maintain quite large and complex societies in medium density cities.

Yet the high-density cities like we have now are exorbitantly wasteful energy wise, and are typical products of our current oil economy. My guess is that most wil lose the bulk of their populations and be torn down to salvage energy expensive materials like copper, aluminium and steel. Perhaps even glass, bricks and cut stone.

I also expect a mayor shift in the infra structure rational, back to the importance of waterways for low energy-high volume, maintenance free, transportation in regions that resource wise can support larger populations. The next epicenter of human civilization will therefore probably lie in the South China Sea region (unless wet bulb temperature rise makes those regions quite unlivable).