I mean we don't know if she knows or doesn't. Like you said it's smth really big to hide and Kiwung is a bit too green flag for that behaviour? (Greener than ml for sure) Kiwung's gf and now wife was just abruptly introduced in the timeskip and we can see that she was well acquainted with mc too, so much so that she'd personally cook for him whenever he comes over. If they all are that close, I think it's safe to say that she would've been sat down and told all about it?
Unfortunately, I remember it all too well. Some things stick in one’s memory far better than one might wish. And, frankly, the way the whole situation ultimately unfolded made me so incredibly angry that it’s etched in my mind. If you look at the situation from the perspective of human psychology, it really doesn’t seem like she’s even aware of what’s going on—her behavior, in fact, points to that. I’m not sure how to put it into words, to be honest, but it’s entirely plausible to assume that she has absolutely no idea about their relationship.

I find it incredibly wrong that the girl doesn't know he's her husband's ex. Overall, this whole arc with the second ML is sickening me because of how... not that it's wrong, but it just feels super unnatural, the way their story unfolded, and yet another reminder of it makes me sick. And the fact that they dragged him into the special, too... Why, just why.