What is the ruling regarding the engagement of the aforementioned girl to another man? Is it permissible to retract a promise to return after divorce? And am I entitled to claim the girl?

Your divorce is valid. If your wife’s iddah has ended, or if she has no iddah, there is no impediment to her engagement and marriage to someone else. The promise made to you does not affect the divorce, nor are you bound by it. As for the woman, she ought to fulfill her promise, but this is not obligatory upon her according to the majority of scholars. If the woman is not willing to marry you, then seek someone else.