The English translation for the Chinese word "剩女", meaning an unmarried girl over 27 without a boyfriend

Yes, "leftover woman" is the correct translation.

It may not be politically correct, or seem polite, but that is the term and it reflects Chinese cultural attitudes towards those women within Mainland China.

The word is used in China and in English-language literature on the subject, including in many peer-review journal articles. See Google Scholar, for example.

Outsiders to China will not likely know the meaning, so depending on your readers, an explanation must be given.

There is not going to be an ideal fit for a neutral version of this term in English. Traditionally, older unmarried women were looked upon negatively So you have older words like spinster and old maid that have strongly negative connotations. There are also adjectives like unmarried and unattached that may come across as negative due to the un- form.

It is only in the last few generations that women living independent and unmarried lives has been widely regarded as neutral, let alone positive, so there are relatively few terms for them. Some collocations (like single woman) are technically fitting, though they don't pertain to a single age. Bachelorette might have fit at one time, though many English speakers will associate that word with the TV show The Bachelorette, which features a woman being taken on dates by a number of competing eligible men. So the neutral options don't exactly fit either.

So if you are translating the term, you may need to decide whether an English translation is sufficient or whether you need to translate literally and gloss the concept, a practice common in academia (JSTOR) but less common in other contexts.

As mentioned by TaliesinMerlin, In English we have the (somewhat dated) term "old maid"...

old maid NOUN
1 derogatory A single woman regarded as too old for marriage.
Lexico

Perhaps a "passed-over" woman, which puts focus on the actions of others, rather than suggesting a deficiency as "left-over" seems to.

Firstly, "leftover" doesn't unambiguously refer to food as in "last night's leftovers in the fridge".

A leftover anything is something that remains. For instance, "Bob went into the building one more time to grab a few leftover boxes and items, and then shut the door for good."

If the "leftover" is turned into a noun, and particularly if subsequently pluralized to "leftovers", then it has a stronger association with food: that word refers to uneaten food more often than not.

Outside of any context, "leftover woman" will not be unambiguously interpreted as an unmarried older woman. It could be a woman left behind in any conceivable situation: "Everyone was rescued from the island, except for one leftover woman."

But in a discussion about unmarried women, if the term is introduced, it will be clear what it refers to; and it will have a negative connotation, laced with sexism, possibly deeply offensive to some people. It has the interpretation of insinuating that a woman is just an item, and one without a husband is just an uncollected or unconsumed item.

"I want to use the word "spinster", but it is a negative word."

But you started this discussion with a negative Chinese word. If that Chinese word has connotations that a woman is just an item, and an unmarried one is just a wasted, unconsumed item, then "leftover woman" actually works. If it doesn't have connotations which are that bad, then "old maid" and such may be more appropriate.

In any case, the job of a translator isn't to produce a sugar-coated version of a text in another language.

Not a direct match, but if she has her own job and life, "career woman" or "career-minded woman" or "single professional woman" might fit.

This is specific to the woman who puts more of her life into her job, and so her single state is her choice, or the result of her being busy, rather than because she is left over. Unlike spinster or old maid (both a bit Jane Austen!) it's not a negative term.

EDIT: The new answer from @aliental seems to support this, and we might add "independent woman" to the choices above, since this does seem to be an official term for a woman making these lifestyle choices. Of course, some career women also have boyfriends, so it's still not a perfect fit.

[ Sheng nu ](it's three words not one!) seems to be a joke rhyme of 剩余 [ shèng yú ], so if it were possible to find a rhyming chide, that would be a good translation. perhaps like a "debris dame", "Lady Leftover". "waste woman". "female fragments" I can't think of a very good one.