What is the ruling on marrying a woman who is referred to as "my wife" and treated as a wife, while being engaged to another woman?

These words do not make the woman your wife, because the pillars of marriage are not complete, which are the formula (offer and acceptance), the guardian, and two witnesses. If the woman is religious and of good character and her waiting period (iddah) has ended, you can propose to her guardian for her hand in marriage. If he agrees, you can then perform the legitimate marriage contract. The mentioned hadith has not been authentically reported from the Prophet, peace and blessings be upon him, with this wording. Rather, it has been narrated with the wording: "Indeed, Allah has people whom He has singled out for blessings for the benefit of His servants. He keeps those blessings with them as long as they expend them; but if they withhold them, He takes them away from them and transfers them to others."