Don’t write the letter. She was honest and straightforward with you, communicated her needs, and is asking you to respect that. Your reaction is to violate that space. And not only that, but do it so you can talk about yourself. Don’t do it. Respect the relationship you had, and when you recognize that connection again with someone else in your life, remember what she told you and try to use it for the next friend.
Also, I’m sorry you’re not treated well by other people who are supposed to lift you up. I hope your future is full of great and storied friendships and that you love yourself to pieces. Your friend gave you what sounds like a great example of making boundaries and only engaging in relationships that are mutually satisfying. All thoughts from an internet stranger, just hoping you take good care of yourself. <3