Does the Prophet's saying, "Indeed, it is forbidden for a suitor to propose to a woman who is already engaged to his brother," apply to a situation where an engagement has ended, and then the suitor returns to propose marriage to the same former fiancée after a period of separation?

What we understand is that the second young man wants to propose to you, and you are asking about the ruling on proposing over an existing proposal, and whether the hadith: "A man should not propose over the proposal of his brother" applies to you.

An engagement is a promise of marriage, and either party has the right to withdraw. The hadiths prohibit proposing over an existing proposal, such as his (peace and blessings of Allah be upon him) saying: "A Muslim is the brother of a Muslim, so it is not lawful for him to buy over the sale of his brother, nor to propose over the proposal of his brother," and his saying: "A Muslim should not bid over the bid of his brother, nor propose over his proposal." The intent is to prohibit proposing to a woman if another person has proposed to her and his proposal was accepted and she became inclined towards him. In such a case, it is not permissible for anyone to propose to her.

Ibn Abi Zayd Al-Maliki said: "No one should propose over the proposal of his brother, nor bid over his bid, and that is when they have come to an agreement and are settled." In Sahih Muslim, it is narrated that Fatimah bint Qays (may Allah be pleased with her) was proposed to by Mu'awiyah, Abu Jahm, and Usamah ibn Zayd. The Prophet (peace and blessings of Allah be upon him) guided her to Usamah. Therefore, there is no harm for this young man to propose to you, as long as you have terminated the first engagement. Choose a person of good character and religiosity, as the Prophet (peace and blessings of Allah be upon him) said: "If there comes to you one whose character and religiosity you are pleased with, then marry him." We also advise against impermissible relationships with non-mahram men except within the framework of a lawful marriage.