There was plenty of character driven change in the episode.
-Pike learns to deal with emotional honesty instead of resisting it.
-Number One shows a stronger sense of belonging, no longer hiding who she is after her trial.
-La’an allows herself to be vulnerable and openly express her feelings, which is a big step for her.
-Spock realizes that leaning into emotion has consequences, pushing him back toward the discipline we associate with his future self.
-Chapel chooses her career and personal growth over the relationship, asserting her independence.
-Uhura leans into her strengths in communication and problem-solving, playing a key role in resolving the crisis.
So yeah, there’s a lot more going on there than just the musical gimmick.