If W has ended her A’s with the OM for good, then does that make her a WAW rather than a WW?
WW is more of a mindset, WW's are rebellious and tend to push away loved ones (including their children) to pursue a GGW lifestyle. WAW's are just kind of "over" their marriage, they just don't want to be married to the LBS anymore and they usually don't even know why. They're just done. But WAW's usually don't push their children away, so at least in my opinion that's usually the biggest litmus test. Now both of them don't consider themselves married anymore after BD. So to them they're not engaging in an "affair" especially if they've already separated. The marriage doesn't exist anymore to them, it's just a nuisance written down on paper somewhere. So while the LBS looks at an affair as a despicable act, to the WAS it's just them "moving on".
With that said, no matter whether she's a WW or WAW the real question isn't "is the A over" because she can easily engage in another or go back to the previous one on a moment's notice. The real question is this- is she invested in making the M work? And of course in your case she's not, which is the point we've been trying to get through to you. She's not trying 100%, or 50%, or 10% or even 1%. She's just not. She doesn't want that right now. Will she ever? That depends on what you do moving forward.