There are nice example how even after human input the translation misses things.
For example, the price of the fish was stated as 2.40 rubles. This is meaningless outside the context and does not explain why it was very expensive for the old man who checked the fish first. But if one knows that this was Soviet SF that was about a life in a small Soviet town of that time, then one also knows that a monthly pension was like 70-80 rubles so the fish cost was a daily income.
Then one needs to remember that the only payment method was cash and people did not go out with amount more than they would expect to spend to minimize the loss in case of thievery etc. and banking was non-existing in practice so people hold the savings in cash at home. That explains why Lozhkin went to home for the money.
Would you want a translator to somehow jam that context into the story? Otherwise, I fail to see how it's an issue of translation.
If I had learned Russian and read the story in the original language, I would be in the same position regardless.
It's pretty common for translators to do exactly that, usually via either footnotes or context created by deliberate word choice. Read classical translations for example and they'll often point out wordplay in the original language that doesn't quite work in translation. I've even seen that in subtitles.
LLMs tend to imitate that practice, e.g. Gemini seems to be doing that by default in its translations unless you stop it. The result is pretty poor though - it makes trivial things overly verbose and rarely gets the deeper cultural context. The knowledge is clearly here, if you ask it explicitly it does it much better, but the generalization ability is still nowhere near the required level, so it struggles to connect the dots on its own.
I was going to say that I'm not certain the knowledge is there and tried an experiment: If you give it a random bible passage in Greek, can it produce decent critical commentary of it? That's something it's certainly ingested mounds of literature on, both decent and terrible.
Checked with a few notable passages like the household codes and yeah, it does a decent (albeit superficial) job. That's pretty neat.
Sometimes when re-publishing an older text references are added to clarify the meaning that people would miss otherwise from the lack of knowledge of cultural references.
But here there is need to even put a references. A good translation may reword "too expensive!" into "what? I can live the whole day on that!" to address things like that.
Some translators may add notes on the bottom of the page for things like that.
It's going to greatly vary of course. Some will try to culturally adapt things. Maybe convert to dollars, maybe translate to "a day's wages", maybe translate as it is then add an explanatory note.
You might even get a preface explaining important cultural elements of the era.
This is also something that an LLM would be able to easily explain. I'm pretty confident that all 4o-level models know these facts without web search.
Not in my experience. Unless you explicitly prompt and bias that model for that kind of deep answer (which you won't unless you are already experienced in the field) you're going to get some sycophantic superficial dribble that's only slightly better than the wikipedia page.