There is no scientific basis for the claim that the earth could sustain 100+ billion people. These types of unsubstantiated claims are not just false but dangerous, as they suggest there is no need for significant action and change.
Does that mean we've fixed the problems? Far from it.
The number of people is only a really small factor in the damage that people do. One jet-setting westerner does many orders of magnitude more damage than the typical subsistence farmer; and the damage done by subsistence farmers varies quite widely. (Some are causing desertification and chopping down trees)
And of course there are some people doing more good than harm, reducing the population reduces those people too.
No matter what the population is, we have a lot of work to do. Greenhouse gases are the most visible problem; there are lots of others.
Other resources are a separate issue, of course.
I agree with the assertion that humanity is more sustainable (all other things being equal) vegan or vegetarian rather than omnivorous, but it's going to far to suggest we could just swap in humans for livestock.
TLDR : 100+ billions is a hard reach today, but 50+ billions might not impossible
There is approximately 63,824,448 km² or liveable land on earth today.[1]
Let's cut that in half to account for farms/land lost due to global warming/industries/etc... We get 31,912,224km² of land usable for habitation.
Let's assume we cover the remaining with a huge city with the density of Hong Kong (6,690 people/km²). This is for the whole city, not the most populated quarters.
We arrive at a population of 213,492,778,560 people, so twice as much as the parent's estimate, with half of the remaining liveable land usable for farms/industries/wildlife parcs/inefficiencies of repartition...
Would that be enough ? According to a Sweden study [2], we use 1.6 billion hectares (16,000,000 km²) of farmland today, for approximately 7 billions people. It means that for 200 billions, we need 486,857,142 km². That's a huge increase, and currently the Earth can only sustain 44,000,000km² (same source as earlier, FAO), so an order of magnitude lower. According to a study on the effect of diets on land [3], switching to a vegetarian/vegan (not much change in the result) diet allows to cut the land use by ~4. So we're left with 121,714,285 km² of required land : a bit better, but we still fall way short. That's going to be our actual bottleneck.
Let's cut population by 3, and we arrive at ~40,000,000 km² of required land for 66 billions people.
It would be a pretty grim dystopia, that's for sure. Most of nature would be erased, there would be a lot of natural catastrophes, and clearly the Earth would be way less welcoming than it is now.
But 66 billions people on Earth, given 'sufficient' technological (and most notably political) advancements is not completely out of whack, especially if we manage to produce clean energy (or at least clean on Earth) and to radically improve our crops (with genetic engineering, hydroponic culture, exploitation of oceans maybe ?)
Bottom line : this is napkin calculation, a lot of factors have been left out (water to give a main one)
[1] : https://www.quora.com/If-every-person-on-earth-was-to-be-giv... (I know, Quora is not the most reputable source, but it seems decently sourced)
[2] : http://www.fao.org/fileadmin/user_upload/newsroom/docs/en-so...
[3] : https://www.elementascience.org/articles/10.12952/journal.el...
Archologies - Isaac Arther (28:43) https://www.youtube.com/watch?v=TqKQ94DtS54&vl=en
Interesting, I've never heard about this before! But isn't it basically just the question of private vs public transport (cars vs underground), but in vertical dimension?
In fact, there's a growing trend of combining fish farming with hydroponic vegetable farming; circulating water between the plants and fish tanks, monitoring nutrient and bacteria levels, can allow for a non-vegetarian diet.
Granted, they're not going to be the tastiest fish- think tilapia, not salmon. There's a CSA farm doing exactly that in a relatively densely populated suburb not too far from me.
With all of that said, I'm sure that for people who do enjoy seafood, it'd be quite tasty. The business near me was put together with eco-conscious people in mind, so the care they put into farming- nutrients, food for the fish, etc. I'm sure the difference between their fish and wild fish is a good deal smaller than stereotypical farm-vs-wild-caught salmon or what have you.