The earth definitely has a carrying capacity. Our ability to push our food production further doesn’t change this fact. I’ve seen around 10 billion people floated as a food production limit in several places.

Crossing this with climate change, particularly our love of beef and pork, is not easy to disentangle.

We may also never hit that carrying capacity if something else other than food supply limits our population growth—war, disease, artificial barriers to food (wealth inequality).