Man, I can't believe they pulled it off. Not every choice made in the episode was my cup of tea, but my hats go off to them.
I'm not really a musical fan - I wouldn't say I'm a musical hater by any means, but they're not something I go out of my way to look for. But the songs were serviceable to certified bangers, and it turns out everyone on the cast can sing (aside from maybe Babs - M'Benga singing little here makes sense, though. Otherwise, he would have confessed to being a murderer). The penultimate song - the solo by Uhura - was fantastic, though I know Celia Rose Gooding actually has a musical theatre background, so they were saving the best for last. The inclusion of Pelia here was a bit weird to me because she contributed nothing to either the plot or really the singing (I wouldn't expect Carol Kane to have a golden singing voice).
The emotional beats worked well for the characters also. We got a culmination of several character arcs built up across the show to date, with Spock/Chapel and La'an's internal turmoil around Kirk. Also, Uhura getting to reflect upon her own pain. I didn't find the Pike/Batel stuff very convincing, but it seems like they're just setting up Batel to die horribly in the finale anyway, so whatever.
The plot was, of course, total nonsense, but there's no way that a "musical episode" could have a sensical plot. It was either this or something like "a Q did it." All of that is completely forgiven.
Still, even though they hit it out of the park in terms of executing what they wanted to do, some of it didn't work for me. I felt a few of the songs just dragged a bit too long, particularly Una's song to La'an, and La'an's solo. I found myself drifting out of focusing on the episode, reflecting on how different the storytelling is for a musical than a regular drama. Musicals don't show, they tell - the characters just directly say what they're feeling, which you can't get away with in books/movies/TV. This makes sense as shorthand within a musical because things have to move quickly, and that's actually how we get to know the inner voice of the characters. But...the songs here basically told us stuff we already knew about the characters. Yes, there was drama related to the other characters finding out, but from a narrative perspective, we didn't really need the songs to understand what was going on between the characters ourselves. They were just there for fun, which is why - once they made their point - I thought a few overstayed their welcome.
Final thought: The Klingon "boy band" scene was possibly the funniest thing I've ever seen in Trek and will live rent-free in my head for the rest of my life.