The questions you ask about what to say are good ones, and we've all been there asking that very same question. The thing is, I want to try and dispel you from the "do this, achieve that" mentality. What you say is important, and how you say it is equally important, however what matters most of all is WHY you are saying it. And to be honest, when your spouse talks about "hearing you" or "seeing you" (as in, "I see the real you now"), this is what she means. She wants to know what is going on inside of your head. She wants honesty, and transparency, acknowledgment and understanding of the gravity of how your choices and actions demolished her, and some sense of empathy for what she's struggling with now, because of you.
It is like anything else in life. I often use the baseball through a window analogy. When that happens, you just own it, apologize, and do your best to get fixed on your dime. "Gosh mister, I'm so sorry. It was careless of me to be playing so close your house. I'm sorry for the mess and the aggravation this is causing you. It was my fault entirely, so here's my info, just let me know whatever the cost is to fix it and I'll have a check for you ASAP." That's it. There is no pit of shame, there is no defensiveness or deflection of any kind. There is no bargaining or haggling or attacking. A person of integrity simply could not sleep at night until they knew the damage they caused was being acknowledged and addressed. That is the goal, to be someone... better. Someone you can be proud of. And the thing is, when you reach that goal, then knowing what to say and when and how to say it, becomes much more intuitive in nature.
All that being said, you registered fairly recently, so I'm going to assume that D-day was recent as well? (To me, recent is 1 year or less). The only advice I offer in that regard, WS to WS, is to expect extremes in emotions, and for those emotions to "roller coaster" quite a bit, going from days where "looks could kill", to days where she wants to go out and have some fun. Your BS is going through what is probably the most painful process she's ever experienced. Worse yet, since the cause of the trauma was a betrayal, she now also has this sense of... being in quicksand. She doesn't know who to trust because the person she trusted the most just betrayed her. Betrayal makes a person question everything about their lives, are people really who they say they are, did things actually happen the way they remember, or were told? It's constant, and it's exhausting, and since she struggles with trust issues for the moment, that affects her support chain, and removes most tools from her toolbox. She's just trying to find her center again. You can't really help her in that regard, but what you can do is try your best not to make things worse. So if there is any TT left, even if you are 1000% sure it will mean the end of the relationship, just get it out there NOW. If it comes out later, it will be much, much worse.
One last analogy. Imagine that you are the guy whose house was hit by that baseball. Now imagine that instead of taking responsibility and accountability for his actions, the guy says, "Gosh, sorry I guess... I mean, I feel bad for hitting your house, but... you gotta admit, you should expect a few broken windows living this close to a field, right? Maybe you should put a higher fence up or something? Hope it doesn't cost ya too much to fix, because if it did, then I'd really feel bad about myself. Oh well, good night." No one cares how badly the other person feels about themselves unless they take ownership of their actions. And no one wants to be blamed in any way for what was done to them. That is just some advice in general, I am not implying that you personally have done those things, however, they are common with WS's, so I just want you to be aware of them, so that you can avoid them.
So for now, do your best to be there for her when you can be and when she is able to accept it, and to be patient and respectful when she can't. Go to IC if you can, and (some personal advice here, if you have trauma in your past, address that FIRST, or nothing else will matter) work with them on finding your inner self-respect, dignity, empathy, vulnerability, strength, healthy boundaries, coping mechanisms, safe spaces, and anything else that you need to address in order to remove pain from your life. Remove the pain from your own history, and you then can stop reliving it on others. I speak from experience on that one.