Is the intended meaning of "Aal" (family/kindred) in the Salat upon the Prophet Muhammad, peace and blessings be upon him, his followers or the People of his Household?

Scholars have differed in defining who is meant by the "family of the Prophet" (Ahl al-Bayt) when sending blessings upon him. Imam al-Nawawi favored the view that it refers to his entire Ummah (nation), specifically the "Ummah of response," meaning those who follow his religion. He attributed this view to some meticulous scholars. He also mentioned that there are other opinions, including: the Banu Hashim and Banu al-Muttalib, or his household and descendants.