I have found three questions on this topic in the last three weeks! I wonder where the recent interest in the Papal States comes from. Not that I'm complaining, the Papal States offer countless opportunities for discussion on the role of religion, religious institutions, and political power in Italy and Europe.

The Papal States are interesting to talk about, and an interesting topic for a question, because they represent a specific path in the European state building process (I'm mostly stealing from this older answer of mine of mine from a few weeks ago). If we were to drop ourselves into any city in Western Europe in the eleventh century, we could expect to find a largely homogeneous political and governmental structure: a council, of some form or other, would typically exist tracing its origins to the Senatorial-style local governments exported by the Roman Empire. Leading this council would typically be the local bishop. The Papal States emerged when the local Bishop appropriated institutions that exerted power far beyond a single city and its hinterland.

In most of Europe urban governments were co-opted by monarchial authority: over time, the political role of these urban bishops was replaced by a monarch or a monarch's representative (or on other occasions, a locally elected representative acknowledged by the monarch). Cities would go on play an important role in legitimizing the power of european states and european monarchs as these political actors centralized and accumulated authority.

In some places, the centralization process was more efficient than in others. In Germany, for example, centralization was not particularly effective for a long time and cities like Cologne, Mainz, and Trier (unsurprisingly, cities with a a strong Roman past) saw their Bishop grow into a powerful political authority. Rome, probably "most Roman" of all the old Roman cities, the local bishop was able to appropriate an even larger slice of the old imperial authority. While we are still in the neighborhood of the eleventh century: would political, social, and economic life have been all that different in Rome compared to other large Italian cities at this point in time? Probably not.

Part of the Bishop of Rome's later authority did stem from the wide network of the Church, but earlier on the Bishop of Rome's primacy over the Catholic Church was far from a foregone conclusion. This leadership role was earned slowly, over the course of a sequence of conflicts between the "Pope" and "Emperor" (an Emperor who, by this point, no longer sat in Rome but from whom Italians nonetheless never really managed to divest from). More importantly (for this discussion, at least) the Italian insistence on the legal construct of "Empire" contributed to the lack of emergence of a central monarchial figure to supplant the urban Bishops. Sure, individual political dynasties did try to subvert and supplant the Bishop-Council form of government, but there were a few places where they never succeeded: the Maritime Republics for one, but also in the City of Rome.

But while in the Maritime Republics political innovations did take place, in Rome they didn't. This lack of political innovation, or rather political innovation only ever framed in the context of religious authority, would be a major weight on social and economic development in the Papal States: While in the rest of Italy guilds and corporations emerged to regulate economic activity and involve more members of society in the governing process, in Rome instead the power of collegiate institutions like the senate-council apparatus waned as religious authorities appropriated more power. Part of this phenomenon is explained by macro trends on the Italian peninsula: the center of economic activity and population migrated away from the South, deprived of its rich connection to North Africa (and to Greece) and instead moved towards the more self-sustaining river valley of the north, where the mercantile class would enrich themselves connecting the newly prosperous parts of Europe to the ancient riches of the east. But ineffective institutions also ensured that the Papal States would never generate mercantile dynasties to rival those of Florence, Milan, and Venice: as where the other cities had expanded the power the mercantile classes, the Romans had instead expanded the power of the clergy. While early on this had helped the Roman political class grow in power and influence, later on it would make their prosperity increasingly dependent on supporting the apparatus of the church.

This doesn't mean Rome was of bereft of great aristocratic dynasties: they did exist, and not only owned extensive estates outside the city, but also built splendid urban palaces. It would be the Roman Aristocracy that would, from the thirteenth century on, push for military campaigns to expand the borders of the Papal State, citing ancient grants of authority (sometimes dating to the Gothic Wars!) as well as the mechanics of the Bishop-Council system long after they ceased to be relevant in order to justify the subjugation of neighboring communities. This also doesn't mean that there weren't any artists or artisans in Rome: Rome was a major center of the Renaissance. In fact, there was a period when the Roman Aristocracy might have been the most prosperous in Italy, if only because the rest of the peninsula was in the throes of the massively destructive Italian Wars (and this would change once Rome was sacked in 1527).

But ultimately, living in the shadow of the Papacy did lead to a certain complacency among the Roman ruling class. By the nineteenth century cities from Rome to Civitavecchia and Bologna appeared derelict and poor even when compared to the slowly industrializing cities of Italy, the taxation system was so outdated aristocrats were still collecting tithes in the countryside, and the papal government was not even able to field a modern army of any significant size. The people of the Papal States were fundamentally living in a state which had not changed for the past five hundred years. This was good for the class of people who had been prosperous for the past few centuries, not so good for everyone else.

That's not to say there weren't some interesting things happening here and there: the city of Bologna, by virtue of its status of "Second City" of the Papal States, saw resources diverted to developing its University which would become one of the largest and most prominent in Europe. Indeed, Bologna would become an important point of exchange in its role as Central Italy's "gateway" to the north, and in the nineteenth century Bologna's aristocracy would be alone in the Papal States in creating cooperatives interested in introducing modern agricultural techniques imported from abroad (but never, unfortunately, industrialization). Further, the Papacy ensured Rome never lost its primacy in Italian's collective perception of the country's most important city, and the the push to sieze Rome would be a major contributing narrative in the movement for Italian Unification.

To conclude, the specifics of "everyday life," in the Papal States, which you explicitly asked about, are difficult to catalogue (that is why I have avoided doing so). I have instead tried to paint a broad picture of what society might have looked like during the Papal States' existence: a strange political and governmental setup, but one that is historically explainable, although admittedly outdated by the thirteenth or fourteenth century. Economic and cultural life was incomparable to the larger and more prosperous cities of Italy, but nonetheless healthily driven by the resources of the Church apparatus (as well as a predictable amount of cultural osmosis) although this too would stagnate as the industrial era approached.