I believe that one of the reasons why we believe that Kara/ Supergirl’s disguise is terrible, and why we couldn’t understand how Lena didn’t figure it out, it’s because the show was made for us to see both Kara as Supergirl and Supergirl as Kara.
But we forget that Lena did not have this privilege. To her Supergirl was this cold, subdued-anger, ultimate judgment, world on her shoulders figure/symbol. Who had an ever present frown, entitled attitude, brawn for brains, and challenging speech to her enemies.
While on the opposite side was Kara. Smiley, goofy, oblivious, clueless about dangers from both the world and the baggage Lena has.
The only time you see Kara frown (Lena is either not looking) or it’s directed to people who already know who she is eg: Alex, J’onn, Winn and Lena after finding out.
The only time you see Supergirl be goofy, smile or show any hint of personality it’s never near Lena s2-s4. Only towards Alex, J’oon, kids, Winn, Mon-El, Nia, Brainy, M’gan.
Thank you for reading.