[AlotOfReading]

If you pick any particular definition of "collapse", very few will actually meet it (let alone on a timescale of mere years or decades). There's quite a lot of literature on this subject already (e.g. Questioning Collapse), but there's also tens of thousands of years of human history apparently lacking records of anything that could be called a collapse.

As for a specific carrying capacity for the Earth, it should be obvious how impossible such a number is to give without a lot more detail in the question. But if we were to assume 10B global population, it could be done with a population density roughly equivalent to precolumbian California. This is not to suggest that indigenous californians lived in perfect natural harmony, but rather to illustrate how low the numbers actually are. I suspect there's probably many reasonable (though utterly alien) ways of life where that density could be "sustainable". Equally, I suspect there are many ways of life where those numbers are not "sustainable".