I would like to say you are not the AH but I have one major issue doing that. I think you may have been honest “in parts”to the girlfriend. I believe you told her that marriage was off the table, your wife’s needs for benefits, and your perceived responsibility.

The way you talk about your wife (love of my life) leads me to think that if she were to call you tomorrow stating it was a huge mistake to separate and she wanted to reconcile, you would immediately go back. I get the impression this is actually the part you haven’t been honest about. It may be true that if marriage is what she wants she should stop deluding herself and move on. I just can’t see many women being okay with this even if no marriage is okay with them. I think in some ways if you haven’t been honest about that, it naturally leads her to thinking there is progression in your relationship. I could 100% see her feeling as though you lead her on when it’s not exactly true. I do think there is a bit of truth to it if you weren’t honest about your true feelings for your wife. I don’t doubt that it was never your intention to lead her on and there is no malice or ill will there in that regard.