Trinidad exports: Actually, ammonia for agricultural fertiliser, though I believe natural gas is also directly exported. Ammonia is easier to handle (which ... says things), so much as crops represent effective water exports, ammonia is a virtual export of natural gas.

On net ag efficiency: I've ... looked into this somewhat, with Vaclav Smil and Howard & Eugene Odum being generally recommended sources.

One aspect of the ecological approach is to look at plants not so much as inefficient, but as the end result of about 3.5 billion years of process refinement, optimising for numerous characteristics, not simply stored carbohydrate/lipids energy, including diseases, weather, pest, and other tolerances. Much of human ag selective breeding borrows energy from those plant services in favour of food productivity. The result is plants less able to thrive on their own. Optimising fertiliser and watering quantities and schedules also allows greater productivity. How much of that is specifically reliant on additional energy inputs is harder to pin down, though fertilisers pre Haber-Bosch were reliant on accumulated deposits generally moved by sailing ships. We could (if necessary) revert to sail, but those deposits are largely gone.

Looking at annual areal output is a good metric. US productivity actually lags Europe if I recall -- Holland is especially efficient.

On animal energy output levels, athletes are best considered as demonstrating a maximum possible short-term output, not a long-term population average. Particularly in the face of suboptimal nutrition, disease, and injury.

Smil's got an impressive set of tables and charts (making excellent use of logarithmic scales) showing output of humans, various draught and domesticated animals, etc. One factoid I've stored away is that a blue whale has roughly the metabolic output of a tractor-trailer rig. And yes: sustained animal output is pretty sharply limited, across scales: per day, sustained over weeks or months throughout the year, or even over lifetimes. Overexertion or overuse severely curtails output, and peak outputs are not sustainable over long periods. (Something Frederick Taylor rather famously omitted from his "scientific" studies.) Figuring about 25% of a typical human's 2,500 - 3,500 calories gives a range of about 30-45 watts of continuous output.

Note that the acre was originally unit of area derived from a measure of work: the amount of land a farmer and team of oxen could plough in a day. In German: Tagwerk, literally "days' work". The unit was variable (condition of land, soil, oxen, and plough determined tillable area), and represented less than a full day's work as the animals had to be rested and pastured.

(Smil notes that a large waterwheel or windmill, and many early Watt steam engines, delivered about 5-20 horsepower, about 3.7 - 15 kW, of power. And that made a huge difference.)

On carrying capacity net net, one of the most highly recommended sources I've run across (though not yet read) is Joel E. Cohen's How Many People Can the Earth
Support? (https://www.worldcat.org/title/how-many-people-can-the-earth...). My understanding is that he explores the basis and implications of values ranging from < 1 billion to > 1,000 billion, which includes most credible (and possibly some less than) estimates.

One point most serious discussions hammer is that "how many" goes along with "how much", in terms of resources:

I = P * A * T

Environmental impact is a function of population, affluence (resource consumption), and technology (as an inverse).

On energy systems and conversion mechanisms: the interesting thing is how little the story's changed in 50, 75, or even 100 years. We've added fission, and PV's gotten remarkably better. Batteries have improved tremendously. Fusion's still a pipe dream. Otherwise: plants, sun, wind, water, geothermal, waves. Flux per unit area is a very good analysis metric, see the late David MacCay's Renewable Energy Without the Hot Air (http://withouthotair.com)

My suspicion is that direct solar thermal (avoids conversion losses) and CSP power (simple and robust) are likely mainstays. There's been some interesting research into low-tech silicon-fabrication processes, with the Global Village Construction Kit (now apparently rolled into Open Source Ecology / Appropedia) doing some work. Purity and process control are major limitations.

See:

https://www.opensourceecology.org/gvcs/

https://www.appropedia.org/Welcome_to_Appropedia

Among the higher DDG results is your own GitHub laserboot repo:

https://github.com/kragen/laserboot

NB: Technologies with a less than zero efficiency factor remove useful energy from the system. A brake would be an example. Perpetual motion technologies have efficiencies >= 1. Which seems unlikely in practice.

(It's a joke, laugh.)