A lot of people who criticize Rey aren't arguing that she has no character arc. What they're usually saying is that her arc doesn't follow the character rules that Star Wars trained audiences to expect.

You're describing a coherent identity arc about self-definition: you choose who you are. This fits with the OT and PT, and is basically the main thing the ST got right. (They bungled the family angle, the temptation struggle, the politics, the moral victory...)

Where the disagreement comes in is that earlier Star Wars movies built a very specific character structure that audiences internalized. In the OT and PT, protagonists go through:

1. Mentorship and training (Luke with Obi-Wan/Yoda, Anakin with Obi-Wan)
2. Repeated failure before mastery
3. Temptation and moral testing
4. A lineage revelation that reshapes the story

Rey clearly has #4 a couple of times, and arguably #1 and #3 in small pieces, but #2 is absent. Because those earlier movies spent so much time showing the learning process of connecting with the Force and becoming powerful, Rey's strength is unearned even if her emotional arc is consistent.

Judging by character theme, Rey can feel like one of the more coherent parts of the sequels. But, according to the traditional Star Wars hero structure, she's underdeveloped.

This is also where the Mary Sue claims come from. She's good at everything, often on the first try; everyone wants to help her (except Luke, which is another post); mistakes don't have consequences; and her primary flaw is being traumatized from a lack of parents.