It would be an extremely bizarre and possibly unconstitutional thing today for instance to imagine Joe Biden asking John Roberts to go negotiate a treaty with the EU High Representative. Why then were judges used for this purpose, being this involved in political negotiations of such significance, in 1794? Was it a reasonably accepted practice then? And when and how did it stop?
This was not the US of today. This was a collection of under-populated rather insignificant recently-liberated colonies that had an equally-small ruling elite, and many in that elite had multiple jobs. Jay had been a New York lawyer, then was on the New York Corresponding Committee leading to the Revolution, then a NY delegate to the Continental Congress during the War, then President of the Continental Congress ( not a very powerful position, by the way) then Foreign Minster to Spain, then Secretary of Foreign Affairs before and after the Constitution was ratified ( during which he negotiated with England) and also Chief Justice of the Supreme Court, then Governor of New York.
Jay was picked to negotiate a treaty because he had experience trying to do that earlier ( and became very frustrated trying to do that without being given any real power by the Continental Congress). He was appointed to the Supreme Court by Washington because he was a very well-established lawyer. But it should be noted that he was only there for five years- and then left to go be Governor of New York.
Nor would Jay be the only Founding Guy to get put in various jobs. Thomas Jefferson would almost be the Southern equivalent to Jay, being a delegate to the Continental Congress, , then a foreign minister, a secretary of state, a state governor- but would be Vice-President and President of the US instead of a justice of the Supreme Court. Some of this was what you would expect when there's a small pool of qualified people to draw from: like a small town government where there are a number of jobs and few people who can do them. Jefferson was tasked with writing the Declaration of Independence at only the age of 33! And like that small town, sometimes that delegation of tasks was against their will: Ben Franklin, who had many useful skills and a private income, was sent as an ambassador to both England and then France, and then came home to Philadelphia hoping at last to retire to a private life in 1785 to find he had been made, essentially, governor of Pennsylvania. And Jay would be begged to return to the Court in 1800 by John Adams- and would give it a pass.