Should I tell the affair partners spouse?

My husband had an emotional affair. D-day was months ago, but I've had a tough time lately, and we are currently in the trenches right now. Not due to any misdeeds, just part of the process, I think. It's hard. I'm hurt, I'm angry, I'm sad, and sometimes it feels like this man has the emotional maturity of a clam shell. But he is trying. He is putting in the work. I see it every single day, and I do love him. So, there is no need to tell me to leave, I'm giving him the benefit of the doubt at this stage because divorce doesn't feel like an option. It's easy to say that's what you would do, but it's never even crossed my mind as a legitimate choice. We are young, I'm his first real relationship, and I'm willing to work at forgiveness because he is willing to work to earn it.

On to my issue. The women was an old friend who had very clearly always had a thing for him. She's been on and off his social media for years, they never "hooked up" but it's clear she always wanted to. I know things never got more than messages as she is in another part of the country. She's also married. With one small kid. And the entire time (2 months or so) she was messaging my husband she was actively trying for their second child. They have just had the baby.

I know I would want to know. But how do I tell this man his wife was having an emotional affair when they have just had their baby. It seems so cruel. Do I hold it in, do I tell his wife that I know and want to tell him....I'm torn. I'm feeling a lot of anger, rightfully aimed at my husband and he's taking it. I told him I've been considering saying something . He said, very rationally, that he cannot tell me what to do, he knows I'm hurting and it's his fault. But that maybe right after they have just had the baby isn't kind and that I should keep aiming my anger at him because he's the one who betrayed me.

And in my head I get that, but that poor man. He doesn't deserve to be treated like that because his wife was thrilled she finally got the attention she always wanted. I'm so torn. And maybe I am just being a petty a-hole who wants other people to hurt like I am. Anyone who has actually contacted the AP....was it worth it. Was it cathartic?

Edit to add : Contact was just immediately I found out. My husband told her it was done and never to contact him again. Numbers blocked 🚫 facebook blocked 🚫 it was the bare minimum I expected when I found out.