A few ways to approach this.

It seems like when you are her friend, at least in theory, she seems to leave you alone. To me, she likes the idea of you more than the work put in. So you might just consider being friends in name alone and letting her keep the distance herself. Just be really boring, don't reply to texts with more than [boring statement] and just let her decide it's not worth it again.

Another idea is to see what she says in the letter. No one knows what will be put in there until you get it. You might just wait until that happens and repost the letter here.

What I would do, personally, is wait for the letter. Read it, take some time to decide if her message is enough, and then ask if she would like to meet up for coffee.

Then you should just tell her what you said here. That she has not been a friend to you for a long time and she has hurt you with her behavior. That you were hoping to keep it peaceful by slowly fading out, but that you realize that was unfair and you are ending the friendship formally.

That is just how i prefer to do it.