Is it permissible to inform a hesitant suitor that someone else is planning to propose to the same girl, while taking into account the Hadith: "None of you should propose over the proposal of his brother"?

If the intention is to alert one of the two men that the other intends to propose to a woman, there is no harm in that. This does not fall under the prohibition of proposing over another Muslim's proposal, because the prohibition mentioned in the hadith, and agreed upon by scholars, pertains to proposing after acceptance and reassurance, due to the hatred and animosity it can lead to. The point of the prohibition is the occurrence of reassurance. So, if the woman or her guardian has become reassured and consent has been given, it is not permissible for anyone to propose over the one to whom reassurance has been given and with whom consent has been expressed. Indeed, the Prophet, peace and blessings be upon him, proposed for Usama ibn Zayd to Fatimah bint Qays after Muawiyah and Abu Jahm had proposed to her, because she had not yet given reassurance or shown inclination to them.