So there is your question and your subquestion - on the one hand, what lasting did Napoleon’s creation of a Kingdom of Italy have in social and intellectual life on the peninsula, and then your main question on how this manifested specifically in the Papal States.

From your question, you seem well aware that the experience of the Napoleonic Kingdom was very influential for the Italian bourgeoisie. In Italy, as in the rest of industrializing Europe, the emergent middle classes represented a growing group of people with enough schooling to develop a shared cultural background, enhances trough the voracious consumption of media which could range from newspapers, to novels, to theater and entertainment. Under Napoleon, the bourgeoisie had also enjoyed political representation, a more free social and political environment, and opportunities for prestige and power in the Kingdom’s bureaucratic machine. The absense of all these elements post-napoleon lent themselves to the emergence of a “Nationalist” narrative which was absolutely not happy to see the peninsula “Restored” to a fragmented and repressive political landscape.

But if post-Napoleon Italy was governed by reactionism and restoration, “Nationalism” in Italy was itself a reaction (reactionism squared?) which meant different things to different people. The earliest activist groups were aggressive in their pursuit of a republican ideal similar to that which had existed in revolutionary France prior to Napoleons emergence (Mazzini and the Carbonai were the prime example, although there were other groups too). Other later groups adhered to more vague principles of self-determination, believing that the peninsula’s prosperity was being held back by foreign influence (probably the most widespread current at any given time). The cohort of the bourgeoisie which had progressed furthest in the cogs of the Napoleonic administration saw in unification an opportunity to construct a political system which would again reward them (Cavour and many influential individuals of the Piedmontese political establishment by the 1840s were the children of people of this persuasion).

As intellectuals lamented the repressiveness of the restored monarchs, and as the industrialization process swelled the population of cities like Milan and Genoa, unrest and revolt were often the means through which popular discontent manifested itself. Since you’re asking about the Papal States, I’ll point out that Rome was no exception to this discontent: While less industrial than the other large cities of Italy, it was nonetheless a large urban environment where the disgruntled bourgeoisie was able to channel unrest against the reactionary political establishment. The solution proposed was simple: Create a new political and social order by unifying the peninsula.

Thus while the objective of Europe’s great powers at the congress of Vienna had been geopolitical stability, “on the ground” so to speak they were instead faced with unrest and revolt not necessarily against the broader political order (although that, in Italy as elsewhere, certainly played a part) but instead against a more tangibly local state of affairs which the political system they sought to “restore” was ill-suited to addressing. And while in some places revolts were more serious and frequent than others (given the institutional and political characteristics which activists and revolutionaries faced) Italy was certainly a place where this sort of unrest was most serious (culminating in the peninsula unifying, after all). Rome was no exception, and was subject to serious revolts in 1820, and of course famously in 1849, when a short-lived Revolutionary Republic was established in the “eternal city.”

Was the city of Rome a center of the movement for Italian unification? Not really. The harbor of Genoa, at the same time working-class and cosmopolitan, which had been annexed by the Kingdom of Piedmont-Sardinia, was the peninsula's most florid hotbed of revolution; almost as active was the rapidly industrializing city of Milan, and of course the politically florid city of Turin. Within the Papal States themselves, only the bourgeoisie of Bologna (the Papal States’ “Second City”) appeared in some way organized and well-connected to events on the wider peninsula, while their more complacent counterparts in Rome might be described as lulled and groggy from the privileges and excesses which proximity to the papacy granted them. But in their own small way, in 1820 and in 1849 the Romans did organize important revolts. These uprisings didn’t have the momentum which the revolts in say, Milan unleashed in 1848, but they were nonetheless significant additions to the revolutionary narrative which eventually led the political establishment to unify the peninsula.

So given all that, what of your question? What would life actually be like? Well, apart from the unrest discussed above you might be surprised to learn that the Papal States were not a particularly prosperous or socially active place to be. Of all the administrative innovations which the Napoleonic era instituted, only the police apparatus was retained; however over the years and decades it too was allowed to decline and fall into ineffectiveness. Industrialization, which was deeply changing the rest of Europe, was beyond negligible in the Papal States; economic innovation was limited to some activity linked to agricultural innovation in Bologna, but the rest of the States and Rome itself remained just as backwards economically as it was backwards socially. Indeed, outside commentators ranging from British Consuls to Mark Twain’s travelogues, were fairly unified in commenting on the poverty and backwardness of the Papal States’ cities, save of course for Rome, where a sumptuous aristocracy built palaces amidst decaying ruins and commanded an oppressed proletariat (there was a small bourgeoisie, which did manage to push through some economic innovations here and there, including the institution of a stock exchange, but the value of this activity was negligible compared to the leaps being made in other Italian cities, even though on the whole the peninsula did tangibly lag behind the rest of Europe). The Papacy’s censors limited access to the latest operas, plays, and books; which although futile in stopping ideas from traveling in an increasingly interconnected world, did manage to stunt local intellectual life, relegating it to commenting the trends and ideas which emerged in more florid intellectual centers (this repression also contributed to the bourgeoisie's increasing awareness that they were less free than their counterparts elsewhere on the peninsula). So in sum, the Papal States were not a great place to be in the Restoration period.

How did new technologies impact the Papal States? Almost always indirectly: the Papacy had no use for railroads or steam power, given its disinterest in industry. But the small roman bourgeoisie, traveling to the rest of Europe through steamship from the harbor of Civitavecchia and on through the increasingly important harbor of Genoa, must have seen the impact of the railroad and steam power in Piedmont and the Kingdom of Lombardy-Venetia (a constituent realm of the Austrian Empire created by the Congress of Vienna). Over the restoration period, many among the bourgeoisie in Rome mirrored their counterparts in the rest of the peninsula in thinking that unification could be an opportunity to shed the shackles of repression and create a new order which would foster prosperity through unity.

So how did the newly active bourgeoisie, and indeed the rest of the populace, react to the millennia-old borders which had been restored after Napoleon? I think you can ascertain the answer: ideas favoring a new and prosperous power on the peninsula were emerging, and they left no room for the old borders and their reactionary governments. Notions of nationalism were emerging, and while they might have meant different things to different people, for everyone progress required elimination of the old borders. The contention was not the “Why,” but rather the “How.”

There is something to say on the details and tidbits linked to the various currents which emerged fighting for unification: early on, there was an somewhat vocal pro-catholic faction which wanted to see the peninsula united into a sort of confederation under the Papacy! Soon however, others instead argued for the elimination of all the old monarchies and the institution of the Republic. By the 1840s, the consensus fell on unity through Kingdom of Piedmont-Sardinia and its Monarch, who by then represented the path of least resistance and whom the various activists currents hoped could be pushed either one way or the other as the unification process progressed.

In all, unification meant different things to different people. But for many of those people, it represented a significant change to the Papacy and how it expressed power on the Italian peninsula.