My FWH isn't here.....but he'd tell you to let go of the outcome. You're either going to do the work or not. And, even if you do, your BS may opt that it is just too much. There were never any guarantees in your marriage before the A....or you wouldn't have gone there.....and there definitely aren't any now.
That being said....if you do the work....and your BS does their work....you can build something better than you had before. And, if you both are for whatever reason unable to reconcile...you will have grown into a better version of yourself for doing that work. Only you both will know when it is time to call it. I think in some ways it is much harder to heal and stay in the marriage as the BS. After all, you're constantly being triggered by the person sleeping next to you each night. No grand gestures, no one time thing, is going to fix this. For me it was years of a million little things he did. Imperfectly, but with the intention to heal us. A million little things over several years. I had to learn not to attack him, despite him deserving every bit of my wrath. And he had to learn to open up to me in ways he hadn't in the past. We had to learn to work together, lean in together.
You BS likely does love you....and is also reeling. Not trusting you, not trusting themselves. I don't know your story, but it sounds like you might be in that first year or two post discovery.
You will fail. You are human. Your BS will not trust anything you say. Get used to sitting in the discomfort of this. Own it. For the love of all things holy, get yourself into IC and MC with someone who specialized in A recovery. We had great success with a Gottman trained MC. Show your BS what you're doing to be trustworthy and keep doing it even if they don't trust it.
Seeing how my FWH has fundamentally changed made me fall in love with him all over again. It has affected all aspects of our lives, with extended family, dealing with elderly parents, how we come together for our child and for each other. The patience my FWH has now....and ability to be present....is something I cherish.