I've read all the resources numerous times but it all points to letting go, giving up, accepting it and moving on.
I'm not anywhere near ready to do that even though I've tried.
You have part of this right. Yes, let go. You cannot make her do what you want. Yes, accept that this is the situation you have right now. But you do not have to give up or move on. Do, however, move FORWARD. Think of it like you are moving on a path. She is moving on another path (maybe in a tunnel) that is not your path. Maybe your paths will intersect or connect back up at some point, but you cannot know if that will happen or not.
When you move forward, you work on yourself, improve your mindset, your health, make sure you are good in your own skin, with or without her or any other person. If she gets her head on straight and wants to work on the marriage, you are in a good place. If she does not, you are in a good place. If you end up finding someone else or not, you are in a good place. All of that has zero to do with giving up or moving on. It has to do with taking care of yourself, making you the best you for yourself. Not for anyone else, but for you.
Hanging on with the attitude that you can "nice" or polite her back, or even just "not scare her away" helps no one. It does not help you, it does not help her. You can still be polite if you want to, but only if it is not hurtful to you. You matter.
You don't have to stop standing for your marriage to take care of yourself and keep moving down the metaphorical road. How would you feel if she arrived at the end of the road, and you weren't there because you stayed stuck?
Little anecdote. I went out to Denny's with (at the time) soon to be XH to figure the split of the assets. As we sit there, he is telling me all about how upset he is that a friends father has died (this happened several month previous, so was not new news). The he stops and says "I don't know why I am telling you all this." I said "I am the one you told all these things to for 20 some years. Why would you stop now?" And it was exactly that. I was the familiar face he always told these things to. It meant zero to him. Zilch. Nada. I was just familiar. I could have been rude, but chose not to, there was no point in being rude. He had no concept of how what he had done had devastated me. He did not care, all he cared about was himself.
This is your W. It's not good or bad that she "reached out" to you. She just needed someone to talk to, you know her and her mother, you are familiar. She needs to manage her image that she is not a bad person. That's all it is.
As to you, respond if that is who you are and it does not hurt you. If it hurts you, do not respond. Place zero importance on anything she does, because guaranteed, she is placing zero importance on you.