As someone who was once a teenage girl, I can say that she's probably just trying to find her own sense of independence and feels self-conscious and awkward talking about what she's going through. Especially when it comes to relationships/sex/"girl stuff", it can be a lot easier to talk to a female role model simply because they can relate specifically to the unique experience of a girl. I wouldn't take it personally (though I'm sure that's hard).
That whole note thing must've hurt though. I'm sorry. It may have less to do with you specifically, and more to do with how our society views moms vs dads.
Your daughter definitely needs you, whether she acts that way or not... especially considering the fact that it sounds like her mental health is a lot better directly because of you and your experience. I'm sure you know that's often a lifelong struggle.
Pretty soon she'll be dealing with the responsibilities and shittiness of the "real world" and will need guidance from you. But at 15, she's really in the thick of puberty, and it's probably really fucking rough at times, so it makes sense that she's being distant.
I'm not a parent, so take this advice with a grain of salt. I'd suggest asking more "casual" questions instead of trying to approach her with a specific topic or agenda in mind... that lets her know that you want to know what's going on with her, but that you aren't necessarily going out of your way to impart wisdom or teach her some kind of lesson. She probably wants to feel more like an adult and would rather ask for advice than receive it unprompted. I remember being annoyed with adults for telling me things that I felt I already knew... if that makes sense. Sometimes it can feel a little infantilizing.
You probably already know this, but you should refrain all judgement when speaking with her. Never minimize her struggles or trivialize her hobbies or interests. That's incredibly important if you want her to want to talk to you. :)
Anyway, it sounds like you're a great dad. If not now, one day she'll probably be really appreciative of everything you've done for her.