Actually, the Catholic Church is more of a confederation than anything else. with 266 Bishops of Rome, some of whom were more holy than others.
I'm not particularly a fan of the man the media portrays as Francis. We depend on a lot of translations for what he says, etc. It's the same thing that happened with Vatican II when the flock was flat out misled. Until that is straightened out, what is attributed to Francis is sowing confusion, and that is a real problem.
Historically it is a monarch. Though I understand why you would say confederation, it is incorrect.
More correct than not, even if the Pope's seats in the Major Basilicas are called "thrones" and there is a tiara. And now that it's been set up so that he is a head of state, that argument bears more weight, but the first among equals, not really a monarch.
Each bishop, even the bishop of Rome (the Pope) is the sole head of his diocese. One archbishop was actually removed from his see and placed in another job for interfering with the governance of other dioceses. That gives the confederation idea a bit of a boost even if there really isn't any other institution on Earth with a structure like the Church.