Remember the mantra is actions not words.......I would not offer up words unless she presses.
No...you do not want to climb with her.
There is no reason to hug her or for that matter contact her.
When she asks if you are ok.....yes, I am doing great. Offer nothing more...if she asks what's going on keep it vague.
I agree with C you made that statement out of anger but that's ok don't sweat it. If she asks what you need moving forward just a simple I am fine, I am doing well and don't need anything thanks for asking. I gotta run now take care.
Always end the conversation don't hang around or linger.
Years from now you might be able to be cordial but that is pipe dream right now. She is carrying guilt and is trying smooth things over.
Since you are separated the only action you have is to completely go as dark as you can until you are tired of limbo and get to the point that your ready to file yourself.