What is the ruling on swearing an oath on the Qur'an and then breaking it, what is its expiation, especially if the same transgressions that one swore not to repeat are repeated?

Your oath on the Mushaf is considered a binding oath, which necessitates an expiation of an oath: feeding ten poor people, or clothing them, or emancipating a slave. If you cannot find these, then fasting for three days. You must also hasten to sincere repentance, as your fiancé is a stranger (non-mahram) until the valid marriage contract is concluded.