Sean,
It is good you want to forgive and reconcile! I hope for the best for you two. It is do-able and if you are both committed to it it will likely be successful.
At the same time, don't ignore the advice here that has been forged over time by many with deep experience of infidelity. A universal principle here is to avoid rugsweeping. Rugsweeping is when you push the issue aside without doing the real work to heal, become safe and restore boundaries that will protect your marriage.
Many Christians may be tempted to rugsweep because of our belief in forgiveness. But any sober minded individual reading the Gospels will see that Christ was no rugsweeper. He addressed issues head on with courage and conviction. "Go and sin no more". Rugsweeping does not help someone "sin no more". It keeps the door open to temptation, resentment and dissatisfaction.
Forgiveness and building a sound marriage is not going to truly happen if you never address the issues at hand. Your wife strayed. Praying about it is good but prayer without action is foolish. Prayer should inspire action, illuminate action not be a proxy for it.
This site has a lot of tools and guidance for sound, sober action that will truly restore a relationship. You don't have to use every tool here... your situation is unique. Pick the ones that will work best. But rugsweeping and hoping for the best is a very risky path. Love doesn't drop out of the sky and fix everything. Love is action and hard work and scary.
"for love in action is a harsh and dreadful thing compared with love in dreams”
Your wife needs you to hold her accountable. That is the loving response required. It will probably be uncomfortable for you and for her. But without it, you are leaving her alone to fight her temptations and create boundaries where she has already failed. How can that be what a loving husband would do?
I urge you to listen to the people posting here and to choose a few concrete actions that will help hold your wife accountable to her marriage vows. And with the humility you have shown in your posts, it is clear that you are willing to make the same commitments and accountabilities to her as well. I am not sure what the best set of actions are for you, you will have to determine that in the end. But knowing the name of the OM and having her be completely transparent about everything that happened leading up to and including the A has got to be a minimum requirement. Without having this information there is no way you can help hold her accountable to her marriage vows.