The Barbie movie is good and you should see it. It's both entertaining, and a "rich text" that lends itself to many interpretations. Which is to say, good job Greta Gerwig.
But you've probably already seen it, and want some analysis of whether it is "new breakthrough in feminism or was it problematic and bad?" Okay well I am not going to address that shallow question, but there is a lot to say if you're actually watching the movie (and not just reacting to the projections you bring in.) To discuss that, we'll have to ignore all spoilers.
Before I go into the dreaded land of the spoiler, here are some other posts about the movie you may want to read. I don't agree with any of them, but they're good starting points for developing your own reading.
SuperMechaGodzilla: https://docs.google.com/document/d/1-m-uGEUenHDyXIV9BlEaoimiXEnFhrsz_EhgErXwrZA/edit
Balioc: https://balioc.tumblr.com/post/723746172204941312/eh-i-take-your-point-in-many-contexts-its-an
Wild Hunt on the Goddess Inanna: https://wildhunt.org/2023/07/barbie-is-the-new-inanna.html
and the Schmidtian version of the Heroine's Journey (not about Barbie specifically, but the fit is obvious) https://heroinejourneys.com/heroine-journey-ii/
Onto my own reading: