(Emotional affair UPDATE) Marriage Unsalvageable?

If you look at my post history you'll see that my husband is involved in an emotional affair with his ex gf. I was able to read many text threads between them where he admitted regretting our marriage, she apologized for leaving him and not being ready to settle down, they still love each other and want to give the relationship another try. My husband essentially admitted that he wasn't attracted to me, that I'm controlling and clingy , and if he had it all to do over again he would have made a different decision. I am pretty confident that there has been nothing physical between them. They discussed what divorce might look like for him and he has basically decided that divorce would just be too much of a headache and he "has a lot to lose" meaning our house and other financial entanglements and he's worried about looking bad in front of our families. We have no children because I have not been able to conceive despite trying for many years (I am now 38) and chances are I never will be able to even with ivf.

I have told him that I want to stop trying and we're not having sex and my husband now knows that I know but we haven't discussed the nitty gritty. I do know his ex has told him that his reasons for remaining in the marriage aren't good ones and that he's actually being selfish by staying but I think he just feels guilty and doesn't want to complicate his life. She actually even said at one point that she couldn't promise to keep this a secret from me because this is something I really ought to know. He backpedaled a little in a pretty lukewarm and unconvincing way. I honestly wouldn't be completely shocked if I heard from her.

I can't see their chats anymore because they switched to a different app at one point, but I believe things may have fizzled out because he decided not to leave and behave himself to make his life easier. Personally I don't think this was a case of him exaggerating the negatives of our marriage to get her attention.

I have sought therapy, but I didn't click with the first therapist I saw. I have the unshakable feeling that this isn't something that can be worked out in therapy. I believe that he really wants to be with her more than he does me. He says he just got carried away because she was his first love.

Are there just some things that are complete dealbreakers that make therapy or trying to work things out futile? I honestly don't think my husband understands that the difference between what he's done and said vs. some cheap affair that can be given a second chance for if that makes sense. I realize that I need to have more discussions with him and should see a professional. I'm working on those things but in your opinion , is this situation "second chance worthy"?

Think there is a part of me that is hoping that he really did just get carried a away when he heard from her. We had been having disagreements around the time they got in touch again.