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 show, 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 ago 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 (involuntary, but reflective of genuine emotion) 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.