I definitely have some bias on the issue, but I will try to be as unbiased as possible, but to lay it out so you are aware, I am an Italian from the Veneto region, as a child I was told about how good unification was and how heroic we had been and that kind of stuff is hard to consider rationally when you are an adult. And I think this is a general problem when you try to address any question that touches on the nationalist narrative of a country, they are polluted somehow. The documentation suffers from the same issue.

“Diary of a Venetian during the Venetian Revolution” is a great historical document when it comes to day to day life and understanding the media landscape of the time, but as a document to have an unbiased representation of the Austrians is not great, it is shamelessly pro-nationalism and printed during a nationalist government. The same goes for many of the documents I have access to of the period. While if we look at the documents that were printed during the Austrian control, the issue is much the same, there was censorship of the media, and as such if you wanted to print a book on the issue of Italian politics, particularly if it tended to have somewhat of a nationalistic reading of the issue ( which in 1800 was hard to avoid), you had to go to Tuscany and print it there, and it would still come out looking like this…

Concluded this preamble here is my opinion

My impression is that Venice was largely as well connected to the independence issue as the rest of Italy. The Habsburgs controlled a lot of Italy, not just Venice. They controlled Lombardy-Venetia, which I don’t think coincidently were the one that revolted the most, and Tuscany.

The truth is that the main driver of Italian independence was probably the liberal public opinion of the wealthy middle classes, so actually, the Lombardy-Venetia area was more involved in the independence issue than much of the rest of Italy.

In January 1848, Manin and Tommaseo ( they will have really important roles later on). Two Italian nationalists get imprisoned by the Austrian authorities. At the time both of them were not thinking of a violent revolution yet. These were some of the demands Manin had made previous to its imprisonment: development of traffic, finances, the Army and the Navy in a "truly national and Italian" key, freedom of speech, entry into the Italian Customs League, the abolition of feudal privileges that hindered agriculture, the emancipation of the Jews, reform of the law.

Anyway in 1848 Venice together with 4 major Italian cities revolted. The revolution started in Milan, which is not surprising because they were in Italy probably the city with the most well-formed liberal public opinion. The 5 days of Milan were bloody and terrible and that is when the revolution started brewing in Venice. Initially Venetian were more willing to take part in symbolic acts of resistance, like wearing certain colors or not buying certain products that went in the Habsburg state coffins.

On March 17 all hell broke loose, news had come that the government of Vienna had collapsed Manin and Tommaseo were liberated. Manin at this point requested the formation of a city guard, and the Austrian authorities, stunned were forced to give it to him.

That later turned into a full-blown revolution in March 22. Manin encouraged by the events in Milan and after the killing of 8 people in Piazza San Marco, he is convinced of the need for a revolution. With the support of some elements of the Navy (mainly Italian) and the arsenalotti, he took over the arsenal, driving out the contingent and the Austrian. Manin then declared the republic. The revolution lasted more or less a year and while all other Italian cities slowly gave up the fight, Venice was basically starved to surrender.

Now the question of the class divide: Let's start with Venice, which is where I have more documents, and then move to the mainland. Because they are two different contexts

According to Ginsborg (Daniele Manin and the Venetian Revolution of 1848-49 pag 124), it was relatively easy to convince Arsenalotti (people working in the arsenal and basically a large constituent of the Venetian working class) to convince them to revolt against the Austrians. The same went for Italian soldiers in the Austrian military, that lamented strict and long service

While the upper middle class in northeast Italy, was composed mostly by people like Manin, Tommaseo, and Trivulzio. They composed the famous liberal and nationalist public opinion. I have less data when it comes to the aristocracy, so I won’t discuss it much. I know, for example, that an aristocratic friend of Manin had his property taken by the Austrians because of his political affiliations, but I am not sure how much of a common occurrence it was. Indeed, Manin's great talent was bringing every section of the Venitian ( city ) population into the idea of the Italian unification and the revolution. His magic didn't seem to work as well with the mainland though.

In terms of the mainland, the issue is more complicated, when it comes to the middle-class they were exactly like the rest of north-eastern Italy, but according to the Habsburg propaganda the peasantry was in favor of the Habsburgs, In this case, I am inclined to believe at least a certain apathy because its in line with some reports from Italian troops in 1849

In 1860 in the thousand of Garibaldi Veneto was the second most represented contingent, after the frankly ridiculous number of Lombards, that was the prevalent demographic. Among the Venetians you have people like Giorgio Manin, son of Daniele Manin, upper-middle class, basically married to the revolution, had been in any possible Italian unification war or battle imaginable, even though he had pretty serious health problems. Then you have run-of-the-mill urban shopkeepers from Verona like Alpron Giacomo. Then, just in case you are curious the only woman in the mille was Venetian and she was pretty poor, Alberto Espen made a book about her for the Veneto region

The place that really seemed to be much more detached from the issue of unification was Trieste and some of the Adriatic coasts that used to have an Italian linguistic component. So much so that during the Battle of Lissa according to Sondhaus Italians coming from this geographic region tended to be the majority of the Austrian navy ( that fought against the Italian one). While a lot of the Venetian component ( 600 hundred people) had been reduced due to Austrian policies and the revolution

If you want a response to "How close was Venice to the rest of Italy culturally?" you need to give me more specific directions. What do you mean by culturally Italian? Because for now, all I can tell you is that Venice used Italian as bureaucratic language in the government since roughly around 1400 ( like the rest of Italy more or less), and that their educational reform under Gozzi was the one in which for the first time a lot of emphasis was put on Italian rather than Latin even at higher educational levels, and that as far as I know unlike what Manin and the other claimed Austria never made any serious attempts to Germanize Veneto, apart for somethings that were related to German in educational institutions related to the Army