Is it permissible to speak with the aforementioned young man after his engagement, knowing that the questioner does not want to do anything that displeases Allah or wrong his fiancée?

It is not permissible for a man to propose to a woman who has already received a proposal from his brother, because that leads to disputes and enmity. One of the most important objectives of Islamic Law is to spread affection and love among Muslims. For this reason, some scholars have deemed it forbidden for a woman to propose to a man who has already received a proposal from her sister, because it causes enmity and hatred. Therefore, you must leave this man and entrust the matter to Allah, for Allah knows what is best for you.