That's interesting, I didn't know that! What would be used more commonly nowadays?
Maybe 머리가 좋다 is more common but I am not sure if 똑똑하다 is old-fashioned. I definitely disagree that it ever means smartass. What I can say is that, according to the NIKL, it is not usual to use 똑똑하다 to one's elders.
Elsewhere in this course 굉장히 is translated as "really." Here this translation insists on "extremely." After hunting around I would agree with extremely. So where ever you have this translated as "really" you should change it to "extremely," so you are consistent across the course. Thanks! https://glosbe.com/ko/en/굉장히 see also: K.Park, Essential Korean Vocabulary, 2nd Ed., Tuttle 2017, pg 313: very, extremely.