Touching on the actual character moments for a bit here: the events of this episode do not reflect well on Chapel.

She’d been hitting on Spock literally since the beginning of the episode, and openly pining after him for most of that time. Four episodes ago, she winds up breaking down in tears explaining to an alien telephone receptionist how much she cares about him. Two episodes she is extremely distraught when Boimler accidentally lets slip that Spock is famous in the future, and her relationship with him almost certainly will not last. And now, she gets into a three month fellowship that she didn’t think she had much of a chance at, doesn’t say a word to Spock until she has no other choice, and then busts out a musical number about how “free” she feels. What the hell.

We already know Chapel has some problems with commitment, but this is a whole 'nother level. Throwing away a relationship she spent most of this show obsessively wishing for, without any apparent consideration for Spock’s feelings or non-breakup solutions to spending a couple months apart, is just wild. I’m sure the finale will touch on this with a little more nuance than a musical number was likely to give, but whatever else is said this is not a good look.

I interrupted that song very differently. When Boimler spoke with Chapel, she didn’t just realize that her and Spock wouldn’t be together long term but also realized that Boimler didn’t really know her like he knew Spock.

Spock goes on to do amazing things and every detail of his life is recorded in books that people over a century later will read and, essentially, worship him. Chapel isn’t even a cliff note. In her mind, she must feel like she makes no difference and gets down on herself. When she gets the fellowship, it renews her confidence and let’s her know that there is a whole universe of possibilities in front of her.

That was my interpretation of her feelings in the song but I can see others as reading it differently.