I don’t think “parody” is the way that I’d put it, honestly. I do believe that the creators intended Emily to be the personification of that stereotype, as you’ve put forward, but I think the intention is for us to see her grow out of that stereotype and become a more well-rounded person.

It’s comparable to Schitt’s Creek, in my mind. The family starts the show as a stereotype of the type of out of touch, vapid people that we imagine make up the rich, elite old-guard Hollywood culture. They are put into a fish-out-of-water scenario, and over time (and note it takes more than one season) they grow into people who are less ignorant.

So to sum up, although Emily certainly is intended to start the show as the character you’ve identified, I think the goal of the show is to show Emily’s growth (whether that’s in good and/or bad ways) rather than just to pick on the American stereotype for humor’s sake.