The film is quotable and has an iconic performance, but everything outside of the workplace drama is completely disposable, and there's been so much change in the last sixteen years about how fashion and media uses and abuses human bodies, and about toxic workplaces, that there's no reason for the musical to stick to the original as much as it does.
We also don't get a sense in the first twenty minutes of what makes "normal" Andy so special, because the show wastes that time sending up her do-good naivete (secondary problem: this just comes across as "lol! this black person cares about civil rights!", which is bizarre). This also means that we don't get a decent sense of why her relationship with her friend and boyfriend matters - the very first scene they have together is a generic "we're friends and we're poor!" scene, and every other scene is them being annoyed by her job. When they get to the end of the first act and they're singing about how they want the old her back, it's like...why, and who are you?
There's also an issue with tone, which is probably the hardest part of adapting this work. The "cerulean" monologue is a great example, where they just copy it over word-for-word but add a chorus in the background going "oooh, you did it this time" and echoing words like "sweater" and "lumpy" or whatever. It's a big moment in the film, but it's also a quiet, tense one where we come to understand why Miranda is allowed to act like she does. Trying to vamp it up only reduces its power - either change it to make it an actual singable moment, or leave it alone to let the actress flex.
It's also been inflated into a much more broad, fantastical comedy. All the jokes about Paris feel like they're straight out of something unrevivably lame from the last century, and the Emily character has become a hyperactive clown, which takes all the poison out of Andy screwing her over. That could actually turn into something interesting if we're presented with the revelation that we were only seeing her through Andy's eyes and, once Andy comes down at the end, we find out that she's actually a somewhat normal person. Instead, we just get the movie ending, which kinda works in the movie because Blunt performance gives her depth, but the musical's Emily is just manic schtick from start to finish, so there's nothing there.
The most interesting thing about the work (book, movie, musical) is the element of Andy transforming herself and how that leads to her helping Miranda screw over Nigel, who went out of his way to help Andy and, in the musical, opens up to her about his journey. In an ideal adaptation this would be almost Shakespearean, but none of Andy's songs are particularly enlightening and, as noted above, we don't get a good sense of where she's starting from except as a lame caricature of a liberal arts graduate, either in song or in dialogue.
Her big number at the end, where she muses over "what's right for me", is particularly funny, because she just sings "What's right for me, it's time for me to choose what's right for me, what do I want the world to see?" over and over. You've had our attention for over two hours and you still don't know what you want? It's a number that could feasibly work if we'd had a decent glimpse into what truly drives her, so when she's singing about following her dreams we can envision them because we know what they are, but we don't, so it feels like an I Want number that accidentally got put at the very end.
I agree with a lot of the sentiments that they could have done something very interesting with Miranda and the fashion industry struggling to adapt. The fatphobia is still there, if slightly reduced, but basically unquestioned, and on top of that is a bunch of misplaced jousting at wokeism, which, again, reads really weird with a black person in the lead. And then there's Miranda, who gets stuck as a copy of the film version with an 11 o'clock villain number slapped on at the end. It's a halfway decent song, but it gets bogged down by generic jazzy belting, and it doesn't solve the question of how we're supposed to feel about Miranda. If they're able to laser-focus the show on the relationship between her and Andy, it might start to coalesce.