When? The political autonomy of the Papal State (and the papacy itself) fluctuated widely over the centuries.

The answer, at any rate, is typically "Very," and after the mid-eleventh century becomes "Almost Completely" unless the Emperor happened to be in town, when the answer reverts to "Very. But if the Emperor happened to be arguing with the Pope, the Papal State’s autonomy would depend on where the Emperor's army happened to be. It's not exactly simple, especially because these polities (the Papacy, Papal State, and the Empire) don't really exist within a spectrum of sovereignty or political autonomy that we, as modern readers, are used to seeing and understanding.

You might be interested in this answer of mine from six months ago where I embarrassingly forgot to reassure the poster that they could ask however many follow-ups they want, as well as this other that I linked to in the previous answer for around the same time, which might offer some color on the history and geopolitical role of the Papal States as a temporal entity.