Is it permissible to recite the supplication: "O Allah, bless and grant peace upon our master Muhammad, the opener of what was closed, the seal of what preceded, the helper of truth by truth, and the guide to Your straight path," especially with the presence of the word "master" (al-Sayyid), which is said to be one of Allah's Most Beautiful Names?

The dhikr mentioned in the question, "Salat al-Fatih," is an innovation (bid'ah) and it is not permissible to worship Allah with it. There are authentic prophetic remembrances (adhkar) that are sufficient and render it unnecessary. It is permissible to use the term "Sayyid" (Master/Leader) for the Prophet, peace and blessings be upon him, and for some virtuous and revered individuals among humankind. This is abundant in the Sunnah, and the scholars of Najd do not deny it, contrary to some claims.