How do I show compassion?

My now ex gf and I are navigating the end of our relationship and we’re each going through alot of pain.

I’m using the tools SCS provided to manage my emotions (thought downloads, models, holding space for my emotions). She is having moments where her thoughts and emotions are spiraling out of control and creating anxiety.

To get to the exact point, if I get in the pool with her then my emotions start to spin (its all my fault*, I’m a bad person for letting it go on like this, I should have never started this with her, etc etc). If I don’t get in the pool with her she acuses me of not having compassion and gets angry that I’m using the “coaching tools” on her. I have recognized this and stopped offering suggestions and circumstanced based opinions.

I don’t know what that middle ground looks like where I can be compassionate but not get in the pool with her. I think about her situation and her challenges (she has to move out and find a new home etc) and I feel some compassion but I am quickly removed from that when I hear her make statements that are wildly untrue (regarding how hard life will be from now on).

I’m sensing your answer will be along the lines of can you have compassion for her and not get in the pool? I can but maybe I’m resistant to feeling the uncomfortableness because it doesn’t feel very authentic. I do understand I have some frustration feelings that are in the mix from because she points out several areas where I failed and that hurts.

Regarding my earlier comment ‘its all my fault’. I’m taking alot of ownership of this because now that I know what I can do with the thought work, I could have managed the entire relationsip alot better and alot of the issues we had would not have been issues. If I could have managed my emotions better, her anxiety would not have mattered.
I think specifically about that relationship life coach that was on the podcast recently that said it only takes one to save a marriage and I believe that. Had I been able to handle myself alot better, a ton of the core issues would not have been issues and I could have helped her anxiety instead of increasing it.

Thank you.