The United States is roughly 9,629,091 km^2.
If all 6,000,000,000 residents of Earth decided to visit on the same day, we could all spread out at about 623 people per km^2.
This adds nothing to the topic at hand, but I thought you’d all be interested.
The OP asks, how many people can the Earth sustain before THE environment degrades. Well, it won’t ever happen. The environment might evolve and become unfriendly to humans, but big mamma Earth herself can take anything we could possibly throw at her without flinching.
I don’t think it’s appropriate to ask this question as if you were actually concerned for the wellbeing of the planet. She’ll be just fine no matter what we do. Rather, I think, we should concern ourselves with minor issues like food and water shortages among 6 billion bald monkeys.
We aren’t doing much about the problem now because there is not a large enough portion of the population threatened. Once we are truly threatened, simple things like centralization can be achieved. Turn all those bland suburbs back into farm land and take your kids to soccer practice on the roof of a skyscraper. The Mall of America and its parking lot hide how much fertile soil?
Take to the sky and tear up all those freeways. Play a real sport and turn over all the golf courses. People short on water can take a hint and relocate where there’s abundance.
We’re not going to suddenly die off when we hit 7B, 8B, or 10B. Our society will evolve with respect to the restrictions of our habitat or we will reach a ceiling. We don’t have to worry about maintaining a reasonable population density because it will be done for us. If we get out of hand, world wide food shortages will start killing us off until things are back under control.
All we have to do is keep rearranging the furniture until we’ve figured out how to build an addition. Once we’ve successfully annexed Mars, we can move all the sports arenas and toenail clipper factories there.
We’re going to be fine.