How to work effectively with an unpredictable advisor? I'm not sure if many grad students face these struggles, as my advisor is in no way abusive or "bad". In fact, she is extremely nice, but just very unpredictable at times. For instance, the same request or question will elicit a very different response depending on the day, and that's really confusing to navigate. I think predictability is kind of key to any type of managerial work.

In addition, she will also play her cards to get what she want. For instance, the advisor I thought I will have through her actions/words during the rotation period, is different from the advisor I ended up getting (little time to talk about my project now, and doesn't seem to care). This happened again when she was trying to have me stay on longer for a project. I wrote a research proposal, but once she realized I was staying, there was attitude change again. Meetings were post-phoned to the point that we never actually discussed any part of the proposal after two months. Now I'm having second thoughts about the whole thing, but would it seem immature to back out of it now? In general, I can't figure out if this is acceptable behaviour, and if I'm just not learning the best way of handling it.
She is a new professor, new to the job. Sometimes it may help to give her a indication what you would need from her, very diplomatic, very polite, but clear. If she does not follow up on that, consider switching supervisors. It is fine to back out from a supervisor that doesn't do their job well and do not promise to improve. It is your right to know what to expect from a supervision.