I'm going to give you exactly the same advice as I would give a woman in your position.
You are taking way too much responsibility here.
You've been very honest about the way your relationship started and I do think it's significant. I wonder whether you actually had different views on infidelity and whereas you perhaps, while not regretting the relationshp with your wife, came to the view that infidelity itself is never justified, whereas your wife believed that it is, in some circumstances and that all is fair in love and war?
The conversations you had in the past about infidelity and the ones you'll have in the future are hugely important, because you need to be on the same page.
If you've ever seen any of my posts, you might have seen me outline the chronology of an affair. In this I state that there are two whole phases before an affair starts; the friendship/mirroring stage and the pre-affair permission giving stage. You say that your wife had an emotional connection to this man before the affair started and this doesn't surprise me. I bet it was in existence when she came to say she was heading for another breakdown and was going to "save herself".
In the pre-affair permission giving process, I've often noticed conversations like this occurring between couples, always instigated by the soon-to-be unfaithful spouse. It is the process of setting you up to fail, because believe me, "saving herself" was shorthand for "I'm going to have an affair" and at that point, nothing you could have done would have influenced what happened next. The die was cast.
Whatever problems existed in your marriage, you are not responsible for her infidelity. Your wife's response to your discovery (significant because she got found out and didn't confess) is to keep you in a state of permanent suspense, subtly blame you for her affair and take all the power in this relationship. She has suffered no consequences it seems and intends to continue working alongside her affair partner.
There is no sense of her horror at your pain, sorrow for her actions or any attempts to put things right and make this up to you. Instead it is her making up her mind whether she wants to stay with you.
Please take back your self-respect here. Being so appeasing is going to not only destroy you, but the relationship. She will not respect you while you are making no conditions for staying with her.
It would be an entirely different matter if your wife had confessed, was terribly sorry and was trying to atone for the pain caused. Relationships can survive affairs and I admire you for your resolve to forgive, but not at the cost of your self-respect and dignity.
I'd be really happy to help you unpick the story you are being given about this affair and why it happened, because I think you are being told a different story to the truth here. In fairness to your wife, she might not yet understand aspects of her affair just yet, but you both need honesty here.