J.D. Vance, the Republican nominee, enters the general election as the favorite. For Representative Tim Ryan, the Democrat, Ohio’s sprawling metro areas offer a possible path to victory.LORAIN, Ohio — J.D. Vance’s convincing victory Tuesday in the Republican Senate primary in this red-tinged state may have put an exclamation point on the power of former President Donald J. Trump’s imprimatur among conservative activist voters.But Mr. Vance, the shape-shifting author and venture capitalist — once a Never-Trump antagonist, then an acolyte of the former president — has one possible battlefield left for the general election: the suburbs.That is where Representative Tim Ryan, a Democrat hoping to appeal to establishment Republicans and working-class voters, will have to drive up the vote to overcome conservative shifts in more rural parts of the state. The suburbs are also the places here and across the country where demographics are the most racially and ethnically diverse — and where Republicans are slightly more split, centrists often feel without a party, and many voters are only now awakening to the 2022 midterm cycle.In Lorain, a working-class, industrial city west of Cleveland, some of that budding interest was elicited by Mr. Trump’s sway in this week’s primary elections, and by news of a draft Supreme Court opinion that would overturn a woman’s right to abortion. At her desk at Dye’s Appliances, Tara Ortiz, 43, a co-owner and manager, shuddered over the thought that her daughters were on the verge of losing control over their bodies that she had long taken for granted.Tara Ortiz, who manages an appliance shop in Lorain, Ohio, has not yet chosen a Senate candidate.Brian Kaiser for The New York TimesThe abortion news made the November election more intriguing, said Ms. Ortiz, who added that she was planning to vote when the time comes but had not yet chosen a Senate candidate. Her husband is a major Trump supporter, she added, but she leans Democrat.“I’m for whatever is going to make a better life for my children, and my Tom,” she said, referring to her husband.Understand the Ohio and Indiana Primary ElectionsTrump’s Grip: J.D. Vance’s win in Ohio’s G.O.P. Senate primary was a strong affirmation of the former president’s continued dominance of the Republican Party.How Vance Won: The author of “Hillbilly Elegy” got a big endorsement from Donald J. Trump, but a cable news megaphone and a huge infusion of spending helped pave his way to victory.Ohio Takeaways: It was a good night for Mr. Trump, and not just because of Mr. Vance. Here’s why.Winners and Losers: A progressive challenger was defeated (again) in Ohio, and a Trump-endorsed Pence (not that one) won in Indiana. These were some of the key results.A 20-minute drive east toward Cleveland, where wood-paneled homes give way to mansions alongside Lake Erie, Bay Village is among the suburbs and historically Republican communities across Ohio that have seen something of a liberal shift. Heading into a pharmacy with his 9-year-old son, Michael Edelman, 43, said Mr. Vance’s groundswell of support across the state was “a little terrifying.” But he said he believed Mr. Ryan could still have a path to victory if enough people show up at the ballot box in Ohio’s eight large urban centers.Michael Edelman of Bay Village, Ohio, voted for Tim Ryan in the primary.Brian Kaiser for The New York Times“If rural counties carry the state, he doesn’t stand a chance,” said Mr. Edelman, the director of education at Ideastream Public Media, which runs several local public television and radio stations.To be sure, Mr. Vance enters the general election season heavily favored against Mr. Ryan. Mr. Trump carried Ohio twice in far less favorable political climates, and with inflation surging and gas prices over $4 a gallon, the Buckeye State is not sheltered from the political winds.In Ohio’s old battlegrounds, where union families voted Democratic for generations, and Appalachian voters tended to shift their allegiances and parties, the Trump era appears to have locked down Republican support. Blue-collar counties that hug the Pennsylvania border to the east and Appalachian regions along the West Virginia and Kentucky state lines — which starred in Mr. Vance’s best-selling memoir, “Hillbilly Elegy” — were walls of support for him.“Trump changed the game here,” said Tom McCabe, chairman of the Republican Party in Mahoning County, where a decade ago Republicans were scarce and now they dominate.Representative Tim Ryan, a Democrat, needs to appeal to suburban voters.Jay Laprete/Associated PressRepublican Senate candidate J.D. Vance in Cincinnati after winning the nomination.Maddie McGarvey for The New York TimesFour years ago, Mr. Vance, working as a venture capitalist, was all smiles as he hitched a ride on a three-day bus trip, scouting investment opportunities in Youngstown and Akron, Ohio; Detroit and Flint, Mich.; and South Bend, Ind. — a tour that was organized by none other than Mr. Ryan. Mr. Ryan, at the time, was the popular congressman from Mahoning and Trumbull Counties, eager to show off progress, like the electric vehicle batteries being built in what he called Voltage Valley.That same year, 2018, Senator Sherrod Brown, a Democrat running for re-election, beat his Republican challenger, Jim Renacci, by 21 percentage points in Mahoning County.But in a very short span, the tables have turned. As president, Mr. Trump effectively stole what differentiated Ohio Democrats like Mr. Ryan from their national party — protectionism and heated anti-China rhetoric — while winning over social conservatives, especially conservative Catholics, with his opposition to abortion rights and attacks on immigrants and transgender people.Mr. Trump slipped by Joseph R. Biden Jr. in Mahoning County 50 percent to 48 percent in 2020, and Mr. Vance slid into Mr. Trump’s wake with scalding attacks on the free-trade policies of both parties as well as with anti-China rhetoric every bit as heated as Mr. Ryan’s. Mr. Vance’s biography — the son of a drug-addicted mother, he was raised by his grandmother in hardscrabble Ohio, joined the military and went on to college and Yale Law School — is every bit as compelling as Mr. Ryan’s tales of high school football stardom and a union mother who raised him on her own.“J.D. Vance is the worst possible candidate for the Democrats to go up against,” said Paul Sracic, a political scientist at Youngstown State University who specializes in the voting patterns of blue-collar Ohioans. “Democrats like Ryan because they think he can talk to these working-class voters and get them back. They’re not coming back.”A sign supporting former President Donald J. Trump still stands in Harveysburg, Ohio.Maddie McGarvey for The New York TimesNot everyone likes Mr. Vance in the Mahoning Valley.“He says whatever he has to say to get done whatever he wants to do,” said Hank Zimmerman, 73, a retired union carpenter sipping a $1.25 glass of Genesee beer at the bar of the 90-year-old Golden Dawn on the weathered outskirts of Youngstown. “That’s J.D. Vance.”Understand the 2022 Midterm ElectionsCard 1 of 6Why are these midterms so important? More