Background
Last month, I broke up with my gf, 36, who I was with for over a year, for the second time. During the pandemic, I had broken up with her briefly but later got back together after we both agreed to see if we could work things out.
At the time of the breakup, I told her that, "neither of us is happy and I am not able to envision a future with you. We tried to work it out again but unfortunately it does not seem to be the case.". I did not go into the details on what was different etc. because I did not think it would make any difference and also, knowing her, I thought any further statements would hurt her more.
It was her suggestion that after the breakup, we should continue to be friends. I agreed. Also, together, we share a dog who now spends a few days with me and few days with her.
During our time together, she was already saying I wasn't supportive: For example, if we spoke about her finding a better job, she'd say she couldn't find a good job because her education was not sufficient and that she did not want to ask her parents to help her fund her education. I offered to pay for any education she wanted to pursue which she did not take. She would still say I was not being supportive.
Problem
Recently, some of her messages are more like jabs at me. She seems to think everything I did for her was a lie. There have been instances where she comes to my place and cries and says harsh things like I never thought she was good enough for me etc. Even though I do not agree to that, I do not say anything because I thought she needed to vent her feelings. But these things are happening more frequently and the most recent one was when she told me about securing a scholarship. Before I could tell her that I was happy for her, she said "you can pretend to care for this as well".
I broke up with her and I take the responsibility for that and for hurting her because breakups aren't easy. I cannot feel her pain exactly but I have been broken up with before so I know a little about it. But her saying things like these affect me. When I told her about this once, she simply replied "So many lies, so much deceit". I felt she thought that breaking up with her was some kind of evil plan that I had for her from the beginning. I get angry but I did not say anything.
So, I have tried to explain to her that when she says things that sting it affects me and ask her to understand that my intention was never to hurt her during the relationship. But everytime she takes it or twists my words into something worse. She even adds things that I never said.
My question is: How do I communicate to her that her jabs are affecting me and would like that to stop and also correct her if she brings up things which she thinks I said when I in fact haven't, without turning it into a bigger rather more emotionally painful argument?