When (if ever) to italicize quotation marks/punctuation?

Hi everybody. This is a pretty niche question, but… I’m wondering whether it makes sense to italicize quotation marks and/or punctuation when someone is speaking in dialogue—for example, if someone says, “She did what?”, do you italicize the question mark? Or the quotation mark after it? Or both? What about just “What?” Do the rules change for that?

Thanks so much!