They are still called flats in some parts of the country. My oldest son has the middle floor of a three-floor brownstone outside of Albany, NY. You can call it an apartment or the second-floor flat.
Very interesting to hear, just as the two last contributions to this debate.
As a former student of the English language, who found this debate very enlightening, I‘d like to say thank you to all of you 🙂- and wish you a blessed Sunday, too.