The problem with carrying capacity when it comes to humans is that we aren't depending just on the environment. We are depending (very heavily now and more so as we move forward) on our technology. If we were depending just on the environment, we probably are well past the capacity.

And that makes any calculations sort of useless. Anything that interrupts that technology's availability can cause a negative cycle. I.e. it'll probably just be a bump and we get over it. But it may not. There are so many inter-dependencies, and those are dependent on so many factors, that it's always possible you can have a perfect storm scenario. Even then most of those would not be civilization collapsing scenarios. But they could cause significant collapses.

Also, the higher the population, the more people are likely to be impacted by any man-made or natural disaster. The cost of those things therefore go up at a non-linear rate. And the local infrastructure/technology collapse that occurred because of one of them can be one of those cracks that suddenly spreads in an unexpected way.