Unless I'm mistaken, you've added these two paragraphs since my last comment:
> Whatever quantity Q of entropy in the training data, the total output will be more Q all accounted for. That's true for humans and machines. No shape of possible AGI will give us any output with less Q than the combination of inputs had. The dream that a machine will solve all problems that humanity can't hinges on negating that, which goes against thermodynamics.
Thermodynamics applies to closed systems, which the earth in isolation isn't.
This is why the source material for Shakespeare didn't already exist on Earth in the Cretaceous.
It's also why we've solved loads of problems we used to have, like bubonic plague and long distance communication.
> As it stands, the planet cannot cope with all the entropy we're spreading around.
We're many orders of magnitude away from entropic limits. Global warming is due to the impact on how much more sunlight keeps bouncing around inside the atmosphere, not the direct thermal effect of our power plants.
> It will eventually collapse civilization/the ecosystem, whatever buckles first, from the excess entropy. Because global warming, poverty, or ignorance is just entropy. Disorder. Things not being just so as we need them to be.
Entropy isn't everyday disorder, it's a specific relationship of microstates and macrostates, and you can't usefully infer things when you switch uses.
Poverty is much reduced compared to the historical condition. So is ignorance: we have to specialise these days because there's too much knowledge for any one human to learn.
Entropic collapse is indeed inevitable, but that inevitably is on the scale of 10^18 years or more with only engineering challenges rather than novel scientific breakthroughs (the latter would plausibly increase that to 10^106 if someone can figure out how to use Hawking radiation, but I don't want to divert into why I think that's more than merely an engineering challenge).