How can one act in an engagement that the suitor does not desire, taking into account the nature of the relationship, the parents' stance, societal views, and the repercussions of breaking off the engagement for both parties?

The suitor is a stranger to the fiancée as long as the marriage contract has not been religiously concluded. If the girl is pleasing in her religion and character, do not leave her, for a righteous wife is a great blessing, so rely on Allah. However, if you find yourself unwilling to marry her, consult wise people and seek Allah's guidance through istikhara. If you decide to annul the engagement, there is no sin upon you. If the engagement is broken, the gold known as "al-shabakah" (which is part of the dowry) belongs to the suitor, not the fiancée.