her self discovery is certainly initiated by an uneasy transition point in her life (moving), but i'd argue that geting beyond that discomfort is not the main point of the movie. and for sure, the spirits are mischievous, but they all carry their own baggage that they try to dump on her (sometimes literally), which is what she's directly and figuratively resisting via all the hoop jumping. she's picking and choosing who she's going to be based on what her ancestors (loosely speaking) are trying to foist onto her. the yokai[0] are stuck in the past but she's not, and she must move beyond her ancestral past to escape back into her real life (which is symbolic of her forming the kernel of self identity). this is where your point about the future (and moving forward) dovetails nicely.
in that way spirited away is a story about a young human going through the process of realizing that they are a self-aware and self-actualizing person destined to become an adult (who much couch themselves in family and tradition), and not simply a child who can play and not care about the world (and her parents especially) anymore.
[0]: it's neat to see the parallel with yaoguai, which is the chinese version of these little demons/goblins, as i've more recently been watching wuxia/xianxia dramas.