In “awlā al-nāsi biṣ-ṣalāti ʿalayhi as-sulṭānu,” awlā is an elative, al-nās is its genitive complement, and biṣ-ṣalāh specifies the respect in which precedence applies.
The clause identifies the ruler as the person entitled to lead in that context; it is not about the number of takbirs.