I do apologize for the late reply. I’m only answering now because I didn’t have the time to dig up my copy of Alvise Zorsi’s “Venezia Austriaca” from which to draw and answer (it's a go-to pop history for Venetian history between Napoleon and Unification, although the annotated summary of the Venetian State Archives, available online, is also a useful and more academic way to explore primary documents). Your question is equally interesting and specific! What, precisely, occurred in the immediate aftermath of the Great Council’s vote accepting Napoleon’s terms on May 12th, 1797?

The terms of the Venetian surrender to the French Army of Italy foresaw a “Representative Government” to be constituted to govern the “Provisional Municipality of Venice.” This government consisted of sixty members elected to represent various social classes present in the city (think of divisions along professional and social organizations; a task made easier by the fact that each part of venetian society, from different kinds commerce in the market, to glassblowing, to things like naval insurance contracts, was regulated by its own system of laws and tribunals). This sixty-person elected body was split across eight committees more or less based the model in place in Revolutionary France, with each committee in charge of a different facet of government (public health, commerce, the famous “public safety,” you get the idea). While this government was theoretically tied to Revolutionary France with a treaty of friendship, its decisions were in practice subordinate to the leadership of the French Army of Italy. If the amount of art and gold hauled off from Venice to Paris is any indication (as well as repression of the citizenry opposing the surrender) this government was fundamentally overseeing a military occupation (even though the actual number of French soldiers disembarked in Venice was very small). Local Jacobins and other long-dissatisfied notables were certainly prominent members of the new venetian leadership committee, but the more unsettling phenomenon (for some contemporary commentators at least) was the overarching apathy amongst the previously reigning venetian governing class. For a decade now, the inhabitants of the great palaces along the Grand Canal had adopted a dark and cynical humor regarding the future of the republic, and since the start of the French Revolutionary Wars conversation in the salons turned semi-seriously to the Republic’s inevitable end. Some, notably amongst the officer corps of the small venetian army, as well as some middle-class shopkeepers and artisans, disagreed with this mood and had even stormed across the city armed with muskets with the intent of stopping the ratification of the surrender, but they were repelled by artillery atop the Rialto Bridge manned by the Ducal Palace Guards. Apathy combined with fear of repression meant that no opposition would be raised in the following months when the venetian Committee of Public safety handed over outspoken anti-jacobin notables to French military authorities.

Much more damaging than the seizure of the city’s riches, however, was the constitution of concurrent provisional municipalities on the Republic’s terretory. Not only were the cities of the Venetian mainland released of their bonds to the city, but so were the lagoon communities like Chioggia, Murano, and Burano. Even the city’s eyes on the mainland, Mestre, at the time little more than a watch-post and ferry dock, would receive its own administration. Authorities in the Venetian provinces would hamper and hassle agents of aristocrats who came to collect rents from their estates, while obligations to send grain and other foodstuffs to the former capital were quickly considered null and had to be renegotiated on a private basis. Indeed, with the end of the Republic each of the provinces on the mainland also vied to establish an individual “Treaty of Friendship” with Revolutionary France. Jacobin influence from the Cisalpine Republic recently constituted in neighboring Lombardy on the tail end of French victories also drove an influential narrative exploring the possibility of a revolutionary state that could govern all Italian-speaking peoples, further encouraging leaders on the mainland to isolate their former capital. The Cisalpine Republic’s capital, the city of Milan, was discovering a politically active bourgeoisie eager to turn the city into a center of revolutionary thought and activism with a fervor that would last long after the Revolutionary and Napoleonic eras. On the other hand, the aristocratic dynasties that had once fueled political discourse in Venice would slowly abandon the city, either for the political salons of the energetic Lombard capital or for their agricultural estates on the mainland (a third option also existed: descent into obscurity). It is telling that in the following decades, during Austrian rule, rather than vie for hospitality in a great palace on the Grand Canal, during the social season up-and coming Venetians would instead prefer to rent small rooms overlooking St. Mark’s square in the old Procuratie.

In June of 1797, St. Mark’s square had hosted a bizarre ceremony where the new authorities burned the golden book of the Venetian aristocracy and led dances before a “Republican Arch” in front of a bemused crowd of onlookers. But the uncertainty regarding the city’s fate would last mere months. Already in October, it was made public that Napoleon had reached an agreement for peace with the Austrian Empire. Venice and its former provinces would be ceded to the Austrian Empire (save for Bergamo and Brescia, which are geographically in Lombardy and were instead retained by the Cisalpine Republic). But before the city was formally handed over, the French authorities oversaw a final seizure of the city's resources, confiscating armaments as well as steel casts stored in the Arsenal. The seized material was brought to France lest the Austrians readily use Venice as a boon to rearm themselves themselves and their navy. In mid-January 1798, Austrian troops entered the city.