WASHINGTON — After an uneven start, President Trump’s election-year tour of revenge succeeded in ousting Republican members of Congress, boosting Trump-backed “America First” candidates who beat back the establishment and strengthening his grip on the party.

Meanwhile, Senator Johnson of Wisconsin, the most vulnerable Republican senator up for reelection, will take on his state’s Democratic lieutenant governor in November in one of this year’s most closely watched Senate contests.

And a member of the Squad of progressive lawmakers survived a tough primary challenge from a Democratic rival running on a pro-police platform, while voters in Vermont are poised to send a woman to Congress for the first time in the state’s 231-year history.

Takeaways from election results Tuesday night:

TRUMP’S GRIP

As the midterm primary season reaches its final contests, Mr. Trump’s grip on the Republican Party is strengthening.

In the spring and early summer, his endorsement record, a metric he touts as testament to his enduring popularity, was uneven. In Georgia, a fixation of Mr. Trump’s after top Republican officials rejected his entreaties to overturn the 2020 election, most of the former president’s hand-picked candidates were defeated at the ballot box.

But as the season ground on, his enduring sway is apparent.

Mr. Trump opened August with his slate of vehement election-deniers beating establishment-backed candidates in Arizona.

By the time the race reached Wisconsin on Tuesday, a wealthy Trump-backed businessman, Tim Michels, won the Republican primary for Wisconsin governor. He defeated an establishment backed candidate, the former lieutenant governor, Rebecca Kleefisch.

And in Connecticut on Tuesday, Leora Levy surged to an unexpected victory over a more moderate rival in a liberal-leaning state that has historically drawn moderate GOP candidates. On Monday, just hours after the FBI searched his Florida estate, Mr. Trump held a tele-town hall rally for her. Another rival credited his late endorsement for her win.

Meanwhile, most of the 10 Republican members of Congress who voted to impeach him have either retired or lost. That includes Representative Peter Meijer who lost his race in Michigan last week along with, in Washington State, Representative Jaime Herrera Beutler, who conceded on Tuesday. Representative Elizabeth Cheney, the vice chairwoman of the House January 6 committee investigating Mr. Trump’s efforts to overturn the 2020 election, will be on the Wyoming ballot next week and is widely expected to lose.

Those developments, combined with the rush of support from Republicans after the FBI executed a search warrant at Mr. Trump’s Florida estate on Monday, were clear reminders of his looming presence.

SQUAD VICTORY

Representative Ilhan Omar’s detractors spent heavily to oust the divisive lawmaker and member of the progressive Squad.

They failed. Again.

Ms. Omar narrowly defeated her centrist challenger, a former Minneapolis city councilor, Don Samuels, all but guaranteeing her victory in November in an overwhelmingly Democratic district centered around Minneapolis. It was the second time a well-financed group had mobilized unsuccessfully against her.

Almost since her arrival in Congress, Ms. Omar has attracted bipartisan criticism. First, she drew condemnation after suggesting in 2019 that Israel’s supporters were pushing American lawmakers to take a pledge of “allegiance to a foreign country” and claiming congressional support for Israel was “all about the Benjamins, baby,” which many saw as an antisemitic trope about Jews buying influence.

That drew a $2.5 million negative advertising blitz, which was financed by the pro-Israel lobby, attacking her ahead of the 2020 election.

This year, pro-police groups as well as a mysterious super PAC spent over $750,000 criticizing Ms. Omar and backing Mr. Samuels. His north Minneapolis base suffers from more violent crime than other parts of the city, and he helped organize a campaign to stop sharp cuts in police funding pushed by progressive activists, including Ms. Omar, following the killing of George Floyd by police.

Other members of the Squad — Representatives Cori Bush of Missouri and Rashida Tlaib of Michigan — had easier victories last week.

TOUGH FIGHT IN WISCONSIN SENATE RACE

If you take his word for it, Mr. Johnson shouldn’t be running. The Wisconsin Republican Senator had pledged to step down after two terms, only to reverse himself this year.

Now, after coasting to victory in his primary Tuesday, Mr. Johnson’s reward will be a hard-fought campaign against Lieutenant Governor Mandela Barnes that could determine the balance of power in the narrowly divided Senate. It’s also certain to saturate the airwaves as millions of political advertising dollars flood the state.

It will be the first time Mr. Johnson won’t be running against Senator Feingold, the Democrat he ousted from office and defeated again six years later. He’s also the only Republican senator up for reelection in a state President Biden won in 2020.

The matchup offers a study in contrasts. Mr. Johnson, 67, is a multimillionaire businessman whose father was a corporate treasurer. At 35, Mr. Barnes is close to half his age and the product of a working-class Milwaukee family. He would be the first Black senator from Wisconsin if elected.

Mr. Johnson has the former president’s backing. He has also been a major ally.

After the 2020 election, an aide to Mr. Johnson told Vice President Pence’s staff in a text message that he wanted to hand-deliver to Mr. Pence fake elector votes from his state and neighboring Michigan. Mr. Pence’s staff rebuffed their request.

Mr. Johnson also met with Wisconsin lawmakers in 2021 and talked about dismantling the state’s bipartisan elections commission and having the GOP-controlled Legislature take over presidential and federal elections.

VERMONT’S GLASS CEILING

Vermont has been represented in Congress by white men ever since it became the 14th state to join the union in 1791.

That’s poised to change after state Senate leader Becca Balint advanced from Tuesday’s Democratic primary to face Republican Liam Madden in a general election contest that will determine who will be Vermont’s next representative in the U.S. House.

Vermont is a liberal-leaning state and a Republican last won the seat in 1988, making Ms.Balint the overwhelming favorite in November. If she wins, Balint will not only be the first woman to represent Vermont in Congress, but the first openly gay person, too.

It may seem unusual that such a liberal-leaning state has not elected a woman to Congress. Yet there hasn’t been much opportunity. As the second-least populated state, Vermont gets to send only one representative to the U.S. House.

The current Democratic representative, Peter Welch, has held the seat for the past 15 years, giving it up to run for the Senate. Senator Sanders had it the 15 years before that. And Republican Jim Jeffords also held the seat for 15 years before he was elected to the Senate.

Although the pace of turnover has moved at glacial speed, there is an upside for Ms. Balint: The seat offers a reliable springboard to the U.S. Senate. Mr. Sanders’ term is up in 2024. So far, the 80-year-old has not said whether he intends to run again.