When I was a master student I worked in a PhD proposal with my master's supervisor. I applied with that proposal to obtain a scholarship from the university, however because I did not get the scholarship, and she didn't have money for paying the research expenses for the study I couldn't pursue the project. Recently, checking the university page of my former supervisor, I saw advertised the same proposal I wrote and submitted for the scholarship application, exactly with the same words, same theoretical framework, same research questions, etc., she did not change a thing, and she is now advertising it as a "possible PhD project" for a new student that would like to apply for it (and probably get the money we needed for the research). Is that considered as stealing work? Can I report her somehow? I wrote all the proposal with constant feedback from her so I don't know if that gives her full authorship of it?
It was a proposal, not a publication. The ethics would depend at least a bit on how much she contributed to the effort. But it isn't necessary for her to leave the research undone if you have gone away and she participated. She can certainly follow up on it, even with another student. It would really only be unethical if you brought the proposal to her, relatively complete. In would have been better had she contacted you before proceeding, of course. I don't know if that was possible.
But if you are still in academia, you might be able to get back into this research, even if not as her student. You need to contact her with a request to participate, reminding her of your earlier work on the proposal. You might be able to achieve an authorship position, provided that you continue to contribute. But your past work probably won't be enough.
Note that I'm basing this on the fact that a proposal for research isn't the same as the research being completed. It is a proposal to study something. It is primarily an idea that might go somewhere.
If you can't participate, for whatever reason, you might still be able to get an acknowledgement in whatever results from the idea. You have to ask, of course.
You say you "wrote it with constant feedback from her" which means that intellectual ownership is difficult to disentangle. It is quite possible that s/he totally stole your ideas and there is nothing you can do about it. It is also possible that all the sensible bits resided in fact in their feedback and that you are a being bit big-headed about your contribution. But this kind of theft is extremely common in academia so do not think that I choose their side by default. However, that is what the system will do.
Now, things could be a little bit different if it was all your writing that now appears word for word on their website. Then you could write to their head of department. Who is still very likely to say "Tut tut, it seems Dr so and so has been a bit naughty. My, my. Now run along now little one."
Don't think I am being cynical or blasé. I am just trying to spare you any further heartbreak. Academia is where the politics are the most vicious, because the stakes are so low.