The main thing to consider about the Papal states is that there was a large separation between what the Pope's de jure and de factor power both within and without them was. In many ways, that power mirrored the power the Pope himself had in the Christian world, as well as the origin of the states themselves. These were not a territory molded out of conquest with the will of the centre imposed on them. Their origins lay in the Exarchate of Ravenna, or rather, the remnants of that territory. The Byzantine hold and authority on the territory had been tenuous at best for generations, and the Pope's authority in the territory rose in the vacuum. But it was not really a will imposed. The survival of the Papal states for most of it's existence relied mostly on outside powers' inability to act against them or more directly in the form of protection by said powers.

Because the Pope's control over said territory was always tenuous, there existed ample space for local landowners and lords to exert control, even when the Papacy was at the height of its authority. When that Papacy was divided and weakened, such as during the Avignon period, there was little standing in the way of those lords exerting even more power and independence. Existing under the 'protection' of the Pope gave them enough protections that they wouldn't necessarily declare independence or anything like that, but it meant fewer resources for the Pope in Rome. Rectifying this situation occupied much of the Papacies of the late 15th century onward, and you could say they were quite successful. This will hopefully be covered in your class, but as I mentioned, the Papal States of the 9th-14th centuries were created by being the default largest power in a vacuum combined with a piece of paper that 'legalized' this position. The Papal States of the following centuries was a power using this position to justify actively imposing power over the localities within it's de jure jurisdiction (and beyond).