The American Founders didn't spend much time thinking about Venice, and when they did, they had little good to say.

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Disclaimer: my area is the political thought of the American Founding. I know next to nothing about actual Venetian history. So I can tell you what American writers thought about Venice, but I have no way of evaluating their claims. Very, very few Americans knew Italian and could study these matters; their knowledge of Venice came from hearsay within hearsay.

In the 1700s, it was common to describe politics as being a balance between the "one," the "few," and the "many." For example, the English constitution balanced these three interests between the King, the House of Lords, and the House of Commons.

What made Venice unique was its lack of a royal bloodline, and a total lack of representation of the common people. This left Venice as a pure, unmixed aristocracy. As John Adams wrote, "in Venice, the aristocratical passion for curbing the prince and the people has been carried to its utmost length."

The Founders would have been familiar with Voltaire's commentary on Venice: while its government was "well regulated, stable, and uniform," it suffered from a "radical defect": that "no amount of merit can elevate a simple citizen." By contrast, "the beauty of the English constitution" was that, "since the Commons have a share in the legislature," public honors are "ever open to those who deserve them."

The reason Venice was called a "Republic" was to differentiate it from European monarchies; the Venetian Doge paled in comparison to a king. But several Americans disputed that terminology. In Federalist 39, Madison wrote that to call Venice a "Republic," where "a small body of hereditary nobles" exercise "absolute power over the great body of the people," just shows how careless people are with political labels.

On the whole, the Founders lacked interest in Venice because they didn't think Venice had much to teach them. According to the notes we have, Venetian history was mentioned only twice at the Constitutional Convention. By contrast, the delegates referenced British history around 100 times. The ancient republics, the Netherlands, and Switzerland were all more cited. (See Raoul Narroll, Clio and the Constitution: The Influence of the Study of History on the Federal Convention of 1787).

When the Founders did discuss Venice, their opinions were low. In Jefferson's Notes on the State of Virginia, he argues that despotic rule by a group of people is just as bad as the tyranny of one, mentioning as an aside, "let those who doubt it turn their eyes on the republic of Venice."

John Adams had the same disdain, writing "the republican forms of Poland and Venice" are "much worse ... than the monarchical form in France" prior to the French Revolution. Adams quotes approvingly from an earlier writer who says the Venetian nobles "'do what they please with the people.'" The City of Venice is free enough, but in the rest of Venetian territory, the people are "'extremely oppressed ... living by no law but the arbitrary dictates of the Senate,'"; indeed, it "'seems rather a Junta than a Commonwealth.'" It's no wonder that people in Venice's eastern territories are continually ready to revolt and join the Ottomans.

The fundamental problem with Venice, says Adams, goes all the way back to "a neglect in the beginning to establish three orders" and find "a perfect balance between them." See here if you'd like to see more of what Adams had to say on Venetian history: https://oll.libertyfund.org/titles/adams-the-works-of-john-adams-vol-4#lf1431-04_head_068

In any case, the Founders would dispute your statement that Venice was "the only Republic preceding the US." The consensus view was that Great Britain had one of the most enlightened and republican governments in world history (although radicals like Thomas Paine would dispute this). As Pierce Butler, one of the delegates to the Constitutional Convention put it: “We had before us all the ancient and modern constitutions on record, and none of them was more influential on our judgements than the British in its original purity." Before Britain, the Founders looked admiringly at Republican Rome. These governments put a much greater stamp on American political thought than did Venice.