Am I wrong to think of praying that the engagement of the girl I love changes, believing that engagement is not part of Islam and therefore my prayer does not involve severing ties of kinship, and that my marriage to her will improve my religious commitment?

Studying in mixed-gender universities is not permissible for someone who can find an alternative. One must lower their gaze and guard their limbs. Furthermore, it is not permissible to establish a relationship with a non-mahram woman. Engagement is legislated, but it is not permissible to propose to a woman who is already engaged and has accepted the proposal; rather, it is permissible only if the engagement has been فسخت (dissolved). Your prayer that Allah diverts a girl from her fiancé and makes her yours is an transgression in supplication and is not permissible; it is more severe than envy, as you are seeking to remove a blessing. Occupy yourself with what benefits you, for Allah knows what is good for you, and you do not.