Is the ruler of a state not the Wali al-Amr (guardian/leader), but rather the Wali al-Amr is the one who assumes the caliphate of all Muslims?

Muslims are not required to unite under a single ruler for him to be their ولي الأمر (guardian of their affairs), nor is it a condition for the pledge of allegiance (bay'ah) that the entire nation unite under one Imam. For the characteristics of one whose authority is valid and whose obedience is obligatory, please refer to Fatwa no. 115817.