What is the ruling on denying the Oneness of Allah in Rulership (Tawhid al-Hakimiyyah), and is singling it out as an independent category a departure from the methodology of the Salaf, and under which types of Tawhid does it fall?

The monotheism of governance (Tawhid al-Hakimiyyah) cannot be denied; it is a type of monotheism. It falls under Tawhid al-Rububiyyah (monotheism of Lordship) in that the ultimate ruler is Allah the Almighty, and under Tawhid al-Uluhiyyah (monotheism of worship) in that the servant applies the laws of Allah. Making it a fourth category is baseless, as it is already subsumed under the other three categories.