I do not think we have reached our carrying capacity, but definitely feel we are approaching it. A stable human population for the planet would seem to be one where there is general equality in food and fresh water accessibility for every individual along with little to no strain on other natural resources, and we have far surpassed the point where this could be possible despite our advancements. Humans, whether we recognize it or not, are simply another species in the biosphere. What ultimately distinguishes us from others is technology, which has allowed us to live longer lifespans and have higher standards of living. Advancements in technology have undoubtedly played a role in constantly altering our carrying capacity.
Despite how far humans have come, I feel there is a possibility we may become extinct- not in the next 100 years, but perhaps within 500 years. We can already see actions that are precursors of societal collapse, like those exemplified with the Mayan civilization and Easter Island. The Mayans relied on corn as their major food crop, and deforested much of the land to grow it. We already rely on a few major food crops, most now being genetically modified because we need a larger supply to feed society. Easter Island inhabitants were also wiped out from deforestation and overconsumption of resources. All over the planet we are seeing cases of overconsumption, deforestation, inequality in lifestyles and accessibility to certain necessities of life. History tells us we may be headed in the wrong direction, and if we aren’t careful, may experience a crash like many human civilizations before us.