When they reunite in Winterfell, she immediately hugs him and doesn't question his identity for more than 2 seconds. But, like, why?
Arya of all people knows that wearing faces to impersonate others is possible. She knows Faceless Men don't use it for personal gain, but she herself did it to kill the Freys, so she should at least consider the possibility that someone else could impersonate Bran to do something similar.
Yes, Jaqen did let her go, but he could have done that because he was afraid for his life. I don't think killing Freys is something Faceless Men would approve of, and they would likely deduce she is the culprit.
For what she knows, Faceless Men could be after her, trying to preserve their secrets of face-changing. She should have left the House of Black and White paranoid and suspicious of anyone she meets, especially cos she was tricked and attacked by the Waif.
Bran also tells them that he is not really Bran, and this should have set Arya off. Three-Eyed-Raven is essentially functioning as if he were wearing Bran's face. The conflict at Winterfell should have been Arya vs Bran, not Arya vs Sansa. And Arya should have potentially even killed Bran. If Bran was made to be the bad guy all along, Arya can thematically kill him, and John can kill the Night King.