I remember that conversation! which makes me think that Mr. Gold always knew about his fairytale past but Regina gradually remembered over time.
also, when the EQ showed up at the castle to enact the curse, she asked where is the baby? Not where is Emma? She didn’t even know the name of Snow White and Prince Charming’s daughter. and since Emma is still not convinced that MM and David could be her parents, Regina likely hasn’t made that connection as well. all she knows is that Emma is Henry’s bio-mom.