Personally, I would leave her alone and move on from the friendship. She doesn't seem to want to reconnect because if she did, then she would be more direct in my opinion and what others have mentioned as well. It may seem crappy now but there will be better people in the future to become friends with
I may be able to explain this "push away without explanation" thing as I have done that. This is not for every SEI, but I can explain my thought process for this.
The push is often done after a LONG pattern of issues that have not been explicitly dealt with or expressed. Most of the time, both people are not aware of it. What I mean by that is sometimes the actions that people do don't always bug or hurt me at first. I think they are not doing it to hurt me or it's a one time thing, it gets sweeped under the rug. I don't think about the possibility of the pattern happening in the future. I value harmony more so and I may find it awkward to bring it up. The person may continue the pattern and I don't realize it is hurting me until it strikes a strong nerve that was unknown before. It is kinda like an AHA moment. After that I start feeling the pressure of that kind of pain, I kinda start bring things up to fix the issue. This may be direct or indirect. If you look hard enough, the pattern is there. More often then not, the person doesn't want to fix the issue that is bugging me or it seems the pattern would continue. I imagine the pain and that's when I put the distance. It is much much worse if you try and close the distance after the push away, that can lead to a lot more bitterness. This choice is not made quickly or easily, it is made when there is no other choice left.
I had an longtime EII friend that I was close with who would constantly ghost me and only reappear when she needed me for something. Eventually, I had enough and I had to cut contact and push away. I got a very direct and confused message from her after cutting her off but, it was too late. I didn't care and there was contradicting information. It wasn't worth it enough for me to continue even though for years I would use anyways and means to communicate with her.
We speak. However, we may not be heard. Nothing is worse then not being heard. From there, I would rather choose silence.