Hi, Justin, and welcome to the forum.
I'm feeling your pain, BrotherMan,
and I am so sorry you are in this untenable position. Here is my two cents worth (not that it's necessarily worth even that much):
Your gf is behaving deceptively in her dealings with her new lover, and it is completely reasonable that you are uncomfortable with that. I personally cannot tolerate it when someone says one thing and does another. If I were in your shoes, I would be taking a "time out" while she decides what course of action she wants to pursue.
But (completely IMO) I think it is entirely possible she's already decided, in that she has decided not to decide. And by acting as if there is no issue at hand, she's trying to get you to go alone with her non-decision.
If it were me, I would hold her accountable, and, again, I would insist on a "time out" until she makes a choice. Then again, I might just kick her to the curb now and resolve to invest my time and energy in people who live truthfully.
Because the house of cards she is building cannot long stand.
Sorry to sound so harsh, but the thing is what it is. And of course it's easy for me to say what I'd do. I don't have my heart and 5 years invested in her.
Best of luck to you, whatever you decide.