Setsuna And Nana are fake. Her entire personality, everything she does, is fake.
Nana doesn't really have a sense of identity, since she has to lie to her parents about everything she enjoys. The media she consumes, and the career she wants to pursue, have to be hidden from her parents
Nana knows what they want, and how she'll never catch up to their expectations. Student Council President, perfect grades, being the best role model she can be. She pretends to be all those things to everyone. To her parents, and the rest of the school.
But what about Setsuna? She is everything that she wants to be. An idol, a nerd, everything. Personally, I think this is fake too.
Both sides of her are based on manga tropes. She lies to herself, and centers her behavior and beliefs around different character archetypes. When her glasses shine, she probably practiced that in the mirror. The way she speaks, the cadence, also probably practiced
All of her behaviors are to make her feel like an anime character. It's sort of like Yoshiko, but she's more grounded in reality. The person she is, nameless, is just a husk. She doesn't have a personality outside of her interests, so she bases her life on them instead
It's sad to think about. How she developed this and what that means for who she is deeper under it all. All of her songs about empowerment and her utter joy she feels, at least to me, are another part of how fake she is. Her one dimensionality is what makes her have depth
A lack of identity. I think that is the connecting trait between all of the girls in the Nijigasaki School Idol Club