The Debutante Ball Car works very well as the beginning of Grace's arc of self-improvement.
Because of how quickly she brought them up with Hazel in this episode, and how much she was emotionally affected by just talking about them, and how prominent they were in her tape, we know that Grace's negative experiences with dancing are some of her most defining childhood memories. She wanted her parents to watch her recital and notice her, and they didn't. She saw her group dance class as a chance to bond with kids her own age and make friends, but they rejected her and she lashed out.
The show very clearly connects these experiences to Grace's terrible behavior, because she literally dances when she's being awful.
Once more she is putting on a show in pursuit of belonging and attention and love, but now she's performing as an infallible object of admiration and worship. Much more successful and gratifying, but still not meeting her underlying emotional needs.
In The Debutante Ball Car, Grace is reminded of her younger self by Hazel's longing to join the Apex and be with other kids, and she reminisces about her dance classes. And just when those memories and feelings are coming back, she has a positive experience with dancing.
No instructors or "learning from the best", just a fun bonding activity with three people who know her and like her. She gets to bask in the spotlight while a whole crowd gasps and murmurs about how amazing she is. It's another instance of the second chances theme of season three. Everything that went wrong with her dancing before has gone right this time.
(Sidebar: It comes up a few times that Grace's mom controlled her appearance, including this episode's mention of her making Grace straighten her hair and wear it in an uncomfortable ponytail. So Grace getting to put up her hair the way she wants and wear an outfit she likes that's in "her" colors is another way this is a do-over, and the fact that she bothered to pick multiple accessories and carefully covered the clothes underneath the dress shows how invested she was in the ball.)
It makes sense that Grace, who once was a vulnerable lonely child getting hopeful that her dance classmates could be her friends, would warm up to Hazel and Tuba very quickly after they learned the dance together. And that Grace, who remembered how much it hurt when her classmates rejected her, would have a moment of empathy and regret when she and Simon exclude Tuba from the bonding moment of Hazel joining the Apex.
And Grace being reminded of her underlying emotional needs, and meeting them in a much more positive and healthy way than "recruit kids into my cult and then we all beat people up together", seems to have recalibrated her personal goals. Grace is much more playful and sincere with Hazel going forward. When she snaps at Simon in the next episode she tells him to make his own decisions like she resents him wanting her to be the leader in that moment. And when she's apologizing to him later she admits her number is going down and she was afraid he might think less of her. Overall, she seems less interested in power and control and image, and more interested in having a good time with the group and being friends.
