Cursor cannot distinguish between straight quotes and curly quotes. If discussed with Cursor, it can prove this to itself and objectively admit it has a limitation. It seems to be only able to output straight quotes.
I’ve experienced Cursor accidentally replace curly quotes with straight quotes when editing multiple documents, presumably because it is not changing specific lines in a file, but replacing the whole file with updated content. That is an independent inefficiency, but is why I hit this quote bug.