OK... Consider yourself privileged @
tyred as this will be one of my very few posts with even a hint of seriousness here! (I feel exhausted already..)
The elephant in the room: the girl has issues. Her issues lead her to depression and not the other way round. The evidence of her issues is what you see in the way she treats her partners. Whatever you saw during her depression was just the by-product.
And here is the question: do you really want to get involved with someone like that? Especially considering the fact that you are just getting out of your personal sh*t! Do you really think that she will suddenly become the loving, caring partner she has never been , only because she never met anyone like you!!! And, please, don't get me wrong! I'm not implying you're not a great guy (not that I would it know even if you didn't ). I'm just saying that whatever her issues are, the are still present, strongly manifested even in her current relationship.
Do yourself a favour and stay with her just as a friends. Find yourself a girl that can and will love you. Someone who can bring the happiness and the balance you need and -most likely- deserve.