Do the actions of a man who proposed to me and then suddenly withdrew without giving reasons align with the characteristics of a pious, believing person? And what is the ruling of Islamic law on this act?

An engagement is a promise to marry, not a binding legal contract. It is disliked to break an engagement without a valid reason due to the breach of promise involved. However, if there is a valid reason, it is not disliked for the guardian or the fiancée to break the engagement, as this constitutes self-preservation and consideration for her well-being.

If the fiancé breaks the engagement for a valid reason, there is no sin upon him. If he does so without a valid reason, he has committed something disliked (makruh).