"And how many divisions has the pope?"
The Vatican is a major geopolitical actor. It may not look this way from secularized Canada where the words of the pontiff no longer carry much weight, but when the pope has a clear purpose, the Vatican is a soft-power superpower and the pope's influence spreads far beyond the Vatican's tiny borders.
In recent decades, each pope's positions on social policy and social justice have a significant influence on local politics in a number of regions, and the Vatican's mobile diplomacy keeps the church internationally relevant by either bestowing legitimacy or showing disapproval to political forces across different continents. That's a position usually reserved for superpowers, not for city states with a population of just over 800.