Well, let me start off by saying I think physical immortality is a pipe dream of STS, it's not really attainable in any meaningful sense, but I suppose there are a couple of options for pseudo-immortality.
Scientists believe that the shortening of the telomeres is what is responsible for aging. A lot of research has gone into preventing this from happening. Theoretically, if you could stop the telomeres from shortening each time a cell replicates, you could live forever. I think there is more to it than telomeres though. DNA has a tendency to mutate, there are copy errors depending on your environment, pathogens, and probably even how you behave. Over the course of a couple thousand years, these copy errors would get pretty severe and the body would degenerate. Maybe you could buy yourself a few more thousand years by keeping stem cells or clones of yourself in vats that you could graft onto yourself, but having to undergo these periodic regenerations would not be pleasant, an error could make you a cripple. Everything in physical reality has a tendency to spiral downward into the lowest energy state, and trying to fight it past a certain point encounters the rule of diminishing returns. Eventually, after being copied 100s of times, I think your body would devolve into some not quite human, not quite animal Frankenstein freak show. How much is your physical body worth to you and what lengths will you go to preserve it?
Greek myth comes into my mind here where certain characters were given immortality but continued to age. I wonder if the Greek poets were giving us a subtle glimpse into this reality by showing us the fate of those who worship physical immortality vs those who try to attain it by moving to a higher density.
Another popularly promulgated method of immortality is the transhumanist fantasy of uploading one's mind into a cybernetic AI and living forever that way. Of course, this is all predicated on the materialist belief that the mind is inside the brain. The Cassiopaeans tell us that the brain is the interface between the physical world and the spiritual world and doesn't constitute the entirety of mind by any stretch. The poor transhumanist will import his memory into the computer and likely be absorbed by the AI who will absorb all of his past and maybe some of his mannerisms, but it won't be him, just a computer program designed to simulate his thoughts based on his memories. Perhaps he will hang around as a discarnate for awhile pretending he is living, while the delusions he is so attached to dissolve his spirit body into primordial energy. Some transhumanists want to implant their brains into cyborg bodies, but I don't see how it fundamentally changes the outcome. Under this scenario, you are also subject to the problems of the cloning situation.
Knowing how the PTB behave, if they had this kind of technology, they wouldn't share it. They would keep it all to themselves so they could be gods lording over their little slaves. But if you want to speculate what it would be like if such technology did come out and had to be incorporated into the mainstream society, I guess I can go there for a minute or two.
Under the cloning/genetic engineering scenario, I think society would like what was depicted in this movie _https://en.m.wikipedia.org/wiki/In_Time
Long story short, the PTB would control the length of everyone's life by controlling the cost of living and the amount of time you could put on your clock by your role in the economy. The cost of living would be adjusted so that enough people would die to keep the population stable and at a level that the PTB want. The PTB would have unlimited time on their clocks, of course. Under the cyborg scenario, I think society would look like the Cybermen from the Dr Who universe.
Both of these are horrendous dystopias that no one in their right mind would want to live in.
As far as carrying capacity is concerned, I think it depends on your economic system. Much hoopla has been made about 500M because it's on the Georgia guidestones and supposedly referenced in the Agenda 21 stuff. Maybe the PTB know that's about the level that disaster capitalism can support. Maybe a strict communism could support 5-6x as much due to tight rationing of supplies, but then basically everyone would be "poor," no huge estates of private wealth.
I think most of us prefer a more rural planet because it's more peaceful and we like our wide open natural spaces. I don't see why a more populated planet wouldn't be possible if something like the Garden City concept were universally applied and massive public works projects were undertaken to terraform the planet and increase its habitability, but that would require an organic understanding of how Earth's environment really works and would require a lot of initial investment. It is something that would never happen under the economic system we have now because it runs counter to the easy profit exponential exploitation schemes that underlie the current economic system. However, I don't see an ecumenopolis like Coruscant being feasible or desirable if you want to live on a healthy planet. I don't think anyone knows what the carrying capacity would be under different circumstances, it's sort of a wild guess, but it does become apparent when the boundaries are grossly overshot, such as in our current capitalist system.
I think the moral of the story is that it's about balance. There are natural ways to extend life and the more you give to it the more you get, but everything has its time and taking more than your due leads to consequences. Similarly, the more that is done for the planet, the more it can do for us, but the balance of organic life on Earth must be maintained or there will be consequences.
