(1) The process of creating "a very, very precise and detailed understanding of the actual problem" is something AI is really good at, when partnered with a human. My use of AI tools got immensely better when I figured out that I should be prompting the AI to turn my vague short request into a detailed prompt, and then I spend a few iteration cycles fixing up before asking the agent to do it.
(2) The other problem of managing context is a search and indexing problem, which we are really, really good at and have lots of tools for, but AI is just so new that these tools haven't been adapted or seen wide use yet. If the limitation of the AI was its internal reasoning or training or something, I would be more skeptical. But the limitation seems to be managing, indexing, compressing, searching, and distilling appropriate context. Which is firmly in the domain of solvable, albeit nontrivial problems.
I don't see the information theoretic barrier you refer to. The amount of information an AI can keep in its context window far exceeds what I have easily accessible to my working memory.
But then I suppose I should learn from my own experiences and not try to make information theoretic arguments on HN, since it is in that most terrible state where everyone thinks they understand it because they use "bits" all the time, but in fact the average HN denizen knows less than nothing about it because even their definition of "bit" actively misleads them and that's about all they know.