A few months ago, Wisconsin Democrats were raising plenty of money for this year’s pivotal State Supreme Court election, but they were struggling to persuade their voters to pay much attention.

Wisconsin Republicans had momentum from helping President Trump win their state in November but were on track to be outspent as usual by the more organized Democrats.

Then along came Elon Musk, the world’s richest man, who is both helping direct White House policy and running an outside political operation that has swiftly become the primary vehicle to power pro-Trump candidates.

Months after he spent more than $250 million to return Mr. Trump to office, becoming the 2024 election’s biggest donor, Mr. Musk has shoveled more money than anyone else into the race for control of a court poised to make decisions about abortion rights, redistricting and labor rights in a top battleground state. He has posted about the contest countless times on social media, held a livestream with his chosen candidate and is planning to visit Wisconsin on Sunday evening, two days before the Tuesday election.

In doing so, Mr. Musk has made himself the face of a contest with significant real-world stakes, and turned it into a test of whether rising Democratic anger can eclipse a billionaire’s political machine.

A victory by the liberal candidate, Susan Crawford, would signify a backlash to Mr. Trump and Mr. Musk’s collective stewardship of the country, giving Democrats hope that all is not lost.