COLUMBUS, Ohio — Republicans running for the seat of Ohio’s retiring senator, Rob Portman, appear determined to bury the soft-spoken country-club bonhomie that was once a hallmark of the party in this state, and replace it with the pugilistic brand of conservatism owned by Donald J. Trump and now amplified by the new band of Buckeye bomb throwers.

The race descended into a brutal slugfest as the leading candidates, the author-turned-venture capitalist J.D. Vance, the former state treasurer Josh Mandel and a self-funded businessman, Mike Gibbons, entered the final weekend before Tuesday’s primaries accusing one another of being insufficiently right-wing or disloyal to the man in Mar-a-Lago.

Ohio used to be known for the quiet conservatism of the state’s celebrated former senator George Voinovich and its current governor, Mike DeWine; for the Merlot-swilling happy-warrior days of the former House speaker John A. Boehner; for the moderation of John Kasich, a two-term governor; and for the free-trade, free-market ideology of Mr. Portman himself.

Instead, affections for such Ohio leaders are now being weaponized — in broadsides from the candidates and advertisements by their allies — as evidence that rivals are paying only lip service to Mr. Trump and his angry populism.

“Josh Mandel: Another failed career politician squish,” a new ad from a super PAC supporting Mr. Vance blared on Ohio television sets on Friday, calling Mr. Mandel, who is mounting his third Senate run, a “two-time loser” and “a moderate for the moderates.”

After so much vitriol, Ohio’s primary will begin to shed light on just how much power the former president can still wield from his exile. But in the final days of campaigning, the leading contenders left no doubt about his ideological hold on the party.

At an evangelical church near Dayton on Friday, Mr. Mandel campaigned with Senator Ted Cruz of Texas, who sought to blunt the impact of Mr. Trump’s endorsement of Mr. Vance two weeks ago. “At the end of the day, it’s not going to come down to who endorsed whom,” Mr. Cruz said before he and Mr. Mandel brought an older crowd to its feet with stem-winding paeans to conservatism and criticism of Democrats.

Some in the crowd of more than 100 worried that the endorsement of Mr. Vance had significantly lowered Mr. Mandel’s odds of victory. “I think it went down quite a bit,” said Paul Markowski, a retired police officer in a Trump 2020 cap. He said he had not forgiven Mr. Vance for comments he made in 2016 denouncing Mr. Trump and saying that some of his support was driven by racism.

“I could get over him not supporting Trump,” Mr. Markowski said. “But when he bad-mouthed us, the voters, that pissed me off.”

Mr. Vance, for his part, pressed his attack on Mr. Mandel, who had vied for the former president’s endorsement with ads calling himself “pro-God, pro-gun, pro-Trump.” Mr. Vance’s spokeswoman, Taylor Van Kirk, called Mr. Mandel “a phony, fraud and sellout, who claims to be ‘anti-establishment’ in public, but throws President Trump and the entire MAGA movement under the bus to the establishment behind closed doors.”

In turn, the one Republican who has said the party needs to move on from the former president, State Senator Matt Dolan, castigated Mr. Vance for bringing members of the party’s extremist wing, Representatives Marjorie Taylor Greene of Georgia and Matt Gaetz of Florida, into the state on Saturday — not because of their extreme positions, but because they are “outsiders” who are “telling Ohioans how they should vote.”

In the rush to the right, Mr. Gibbons, who had styled himself a businessman in Mr. Trump’s mold and was once the front-runner in the Senate contest, pledged his fealty to a right-wing movement, called the Convention of States, to rewrite the Constitution to restrain federal power.

All of the major candidates in the Republican Senate primary have insisted they are the true conservatives in the race, but only one, Mr. Vance, has the official imprimatur of the former president. That means the judgment that Republican voters render on Tuesday will go a long way to show whether even conservative candidates like Mr. Mandel and Mr. Gibbons can overcome a cold shoulder from Mar-a-Lago.

“President Trump is a major factor in this state,” said Alex Triantafilou, the longtime chairman of the Hamilton County Republican Party, which includes Cincinnati. “He just is. He still motivates our base in a way that some people think is waning, but it’s not from my perspective.”

Still, to call Tuesday’s Republican primary a referendum on the future of Trumpism — in Ohio and beyond — would go too far. The state’s low-key Republican governor, Mr. DeWine, does not appear to be threatened in his quest for re-election by a primary challenger, Jim Renacci, whose “Putting Ohio First” campaign adopted MAGA themes in its attack on Mr. DeWine’s pandemic-control efforts. Mr. Trump declined to endorse Mr. Renacci, seeing no prospect for victory.

The former president’s attacks did chase the one Ohio Republican who voted to impeach him, Representative Anthony Gonzalez, into retirement, and he buoyed a former White House aide, Max Miller, who is running for an Ohio House seat, despite an accusation from one of Mr. Trump’s press secretaries, Stephanie Grisham, that he had physically abused her.

But in other contests, such as a heated Republican primary in northwest Ohio, mainstream Republicans are expected to prevail against conservative showmen like J.R. Majewski, who painted his vast backyard into a 19,000-square-foot Trump election sign and posted a video of himself walking through a shuttered factory with an assault-style rifle.

In the bellwether Senate race here, however, Mr. Trump’s influence is undeniable. The state was once a reliable birthing ground of center-right Republicans, such as Mr. Portman, Mr. Boehner and Mr. DeWine, who has been in Republican politics for 45 years, as a House member, senator, lieutenant governor, attorney general and governor.

But the free-trade, free-market and pro-legal immigration sentiments that were once hallmarks of the party have been washed away by Trumpism.

And the Ohio primary will kick off a four-week period that will reveal much about Mr. Trump’s sway with the party — and just how transferable his continued popularity is to others. After Ohio, his preferred picks in Nebraska, West Virginia, Pennsylvania, North Carolina and Georgia will all be tested in heated primaries.

Mr. Vance, buoyed by the endorsement bump and leading in a Fox News poll, is scarcely tacking to the center, confident in the support of the Republican base. On Saturday, he will barnstorm through Ohio with two figures from the right fringe of the party, Ms. Greene and Mr. Gaetz. On Sunday and Monday, he will be joined on the campaign trail by two other figures firmly in the former president’s camp, Senator Josh Hawley of Missouri and Charlie Kirk, the bombastic leader of the far-right Turning Point USA.

But after trailing in the primary contest for months, Mr. Vance enters the final stretch as something of a front-runner, with the other candidates training their fire on him.

Providing air cover for Mr. Mandel, the business-backed political action committee the Club for Growth is broadcasting an advertisement repeating attacks that Mr. Vance made in 2016 against Mr. Trump and his supporters, suggesting the former president made a mistake with his endorsement.

A pro-Vance super PAC, heavily funded by Peter Thiel, the Trump-aligned financier that Mr. Vance works for, fired back Friday with an ad running in Columbus, Dayton and Cleveland that portrays Mr. Mandel as a “squish.” Mr. Mandel’s embrace by the Republican nominees for the presidency in 2008 and 2012, John McCain and Mitt Romney, are treated in the advertisement like a scarlet letter, and kind words from Mr. Kasich might as well have come from Nancy Pelosi.

“Josh Mandel, he’s for them, not us,” the narrator intones, a clear message that Tuesday’s primary is geared toward the Republican extremes, not the sort of voters who once backed Mr. Kasich and Mr. Romney.

Mr. Gibbons, still in the hunt for the nomination, will trot out yet another Trump ally, Senator Rand Paul of Kentucky, on Monday to attest to his conservative bona fides. In a series of statements on Friday seemingly issued to appeal to the far right, Mr. Gibbons declared that a “dire need of real change” meant he would support a convention to rewrite the Constitution, and said that a new effort by the Department of Homeland Security to combat disinformation would be “a de facto ‘Ministry of Truth’” to crush dissent.

Jonathan Weisman reported from Columbus, Ohio, and Trip Gabriel from Dayton. Shane Goldmacher and Maggie Haberman contributed reporting.