Did you have a specific accessibility concern?
Screen readers have a "punctuation" setting and most screen readers set the default to "some" (with "all" and "none" being other common options). The punctuation setting can generally be customized so the user can always hear certain symbols. The punctuation setting covers more than standard grammatical punctuation symbols. It includes other symbols too.
For example, commas and periods are not announced in "some" mode. They just cause the screen reader to pause briefly while reading, similar to how you'd do it in your head.
Same thing with parentheses, they cause a brief pause.
Question marks are typically not announced either but they cause an inflection in the screen reader voice so you can tell it's a question.
Quotation marks are somewhere in between. They're often not announced and they don't cause any change in reading inflection or pauses. But quotation marks can be very important to hear so that you know when someone is being quoted. A user might have to specifically turn quotation marks on if they're not included in the "some" or "all" punctuation setting.
And this is where your question comes in. Are "smart quotes" or curly quotes or straight quotes announced differently from each other? Are single quotes announced differently from double quotes?
Each screen reader is different and the different styles would have to be tested with each screen reader. But even if the results aren't what you expect, the user has control over how they should be announced.