Is the stance of the girl's family correct in stipulating that the ownership contract of the apartment be changed from the father to the son, or else the engagement be terminated, knowing that the son did not pay anything for it and it is registered in his father's name?

Marital life is a long journey that may entail some risks. Both parties have the right to dissolve the engagement if it becomes apparent that it is in their best interest not to complete the marriage, or to condition its completion on a specific matter, while dissolution for a reason not considered Islamically valid is disliked. The girl's family did not err in their stance, as it became clear to them that what they were told about the apartment contradicted reality. If you lied, you must repent to Allah. If your father gifted you the apartment and your sister agreed, it should be registered in your name to avoid disputes. If you are unable to register the apartment or if it does not belong to you in the first place, and you tried to convince the girl's family to marry but it did not happen, there are many other women, and perhaps Allah will facilitate someone better for you, in fulfillment of His saying: "But perhaps you hate a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah knows, while you know not" (Al-Baqarah: 216). A Muslim should strive to marry a woman of faith and good character.