Welcome to the boards, but I have to say that I'm sorry to see you here.
I'll give you the perspective of a WS, if you don't mind.
Of course your wife "thinks" that this person is her soul mate, and I'd give it a 99% chance that it's a lie she's sold herself to believe that it's "okay" to do what she is doing. No one would intentionally hurt another that they love, unless it's somehow justified.
I too found myself with a "new soul mate" while I was sinking into my affair. Looking back (and Omg it's already 4 years ago now...) I can't believe how stupid I was.
In your case, you absolutely need a boundary here. There is no possible way for your wife to have two different long term relationships, especially if one is founded on a lie. She will need to choose, and let the chips fall where they may.
This isn't all doom and gloom though. I chose to leave my house, wife...and almost everything behind to be with that "soul mate", only to discover real quick that it was me that had the problem, not my wife# or my AP. It came abundantly clear that the AP wasn't my soul mate because suddenly our relationship had all these hooks in it...jealousy, distrust, conditional love, etc.
I'm lucky that my wife did the 180 mentioned above...it
gave me a chance to really see what I was missing, and that she could move on without me. I recognized quickly that I didn't want to be with this so-called soul mate if it meant that my wife would continue on without me.
I think that's the day I actually got my crap together, grew up, and looked within.
The Tl;Dr of this post is...work on yourself, and hope your wife comes around. Don't push things, but put a boundary there as to what is acceptable and not.
On another note...guys...I know I'm not around much here...but I'm hard at work on the marriage I almost threw away. I'm happy to announce that things have gone back to a semi normal way. The affair is like an old wound, a scar that reminds me of how stupid I can be, especially when I take things for granted.