In short whilst relationships can and do recover from infidelities and betrayals, they are never the same as they once were.
I forgave my DH, it was many years ago and we are still together. The difference being that I don’t blindly trust him as I once did, there is always a small part of me that holds back in self preservation and protection over my own heart I suppose. It’s not something I do out of spite/revenge, I genuinely can’t help it, I can just never be as truly vulnerable or as trusting as I once was.
You’ve made a mistake and whilst I get that these things happen and that you genuinely regret it you’ve further complicated the situation and feelings on this matter for your poor DH because whilst you decided to come clean you still were not completely honest. This will be a major trauma and all around headfuck for him, it’s hard enough dealing with the betrayal but harder still when you don’t know the extent of it, and then end up hearing it from someone else. I’m sure you know you’ve done yourself no favours there.
Having gone through this and been in your husband’s shoes it makes everything feel like it’s been a lie the whole time, the trust and faith you once had in your partner evaporates into thin air and you end up feeling incredibly foolish for a whole host of reasons. You blame yourself, wonder why you weren’t enough, then wonder how blind and stupid you were not to notice certain things, or kick yourself because you did notice but didn’t say anything. At first it feels so heartbreakingly raw you can’t imagine ever getting over it, so many things are hurt, your pride, your trust, your beliefs about the relationship you thought you were in, your confidence shattered, it’s a mess and absolute hell to go through.
My advice...give him space, let him know your genuinely sorry and that you would like to do whatever he deems necessary for you to save the relationship. Once you’ve done that leave him be, don’t push for answers, don’t pressure him, don’t look for ways to place blame for this on him, or for ways to excuse your behaviour. You’ve done a terrible thing and all you can really do is be sorry and be happy and willing to sit there being wrong, knowing what you did was wrong without disputing or excusing it and if he asks questions about what went on regardless of how awkward or uncomfortable it is for you to answer make sure you answer it honestly.
There are no guarantees, you could very well do all of the above and it still may not be enough, sometimes things just can’t be saved.