Texas is holding the first primary election of 2022 on Tuesday. Some of the dynamics at play include the intensity of Donald Trump’s continued hold on the Republican electorate.HOUSTON — The Texas primaries on Tuesday will provide the first pieces of the 2022 midterm puzzle.The strength of the two parties’ ideological factions. The intensity of Donald J. Trump’s continued hold on the Republican electorate. And, for bullish Republicans, the earliest signs of how advantageous the political climate has become.The full picture of the 2022 landscape will be revealed through a series of state-by-state primaries held over the next six months. But the country’s first primary elections in Texas represent almost a sneak peek of many of the coming dynamics nationwide in an increasingly challenging environment for President Biden and the Democrats. That includes the impact of strict new voting rules imposed by the Republican-controlled Texas Legislature and the political salience of abortion for both parties.A Texas state law last year effectively banned most abortions after six weeks of pregnancy, and this year a ruling from the U.S. Supreme Court is expected in the Mississippi abortion case, which could affect procedures in multiple states. In South Texas, progressives are attempting to defeat one of the last anti-abortion Democrats remaining in Congress, Representative Henry Cuellar, and they received a political gift when the F.B.I. recently raided his home. Falling short under those circumstances would be a blow for the left after Mr. Cuellar narrowly won two years ago.At the top of the ticket, Gov. Greg Abbott, a Republican, is widely expected to vault past two spirited right-wing challengers. But he is also likely to come nowhere close to the 90 percent he marshaled in his last primary four years ago, a testament to an increasingly restive Republican base.Mr. Abbott has aggressively catered to that base over the last year and in the campaign’s closing days, telling state agencies to investigate treatment for transgender adolescents as “child abuse” and suggesting he might pardon more than a dozen Austin police officers who were indicted on charges of using excessive force during racial justice protests in 2020.“Governor Abbott is running very hard and taking the campaign very, very seriously,” said Ray Sullivan, a Republican strategist who served under two Texas governors, Rick Perry and George W. Bush. “There is an ongoing battle: the mainstream conservatives versus more right-wing, more conspiratorial and paranoid voices. Some of the primary elections will help determine where the energy is in the party.”After redistricting, Texas lawmakers erased nearly all the House seats that were competitive in the general election from the map in 2022, magnifying the importance of a handful of contested primaries in both parties. Republicans, in particular, are hoping to build on the dramatic gains the party made in South Texas and the Rio Grande Valley, particularly among working-class Latino voters in 2020, in the state’s lone open, tossup seat.Nationwide, Republicans are energized by the chance to take back both the House, which the Democrats control by a historically narrow margin, and the Senate, which is equally divided with only Vice President Kamala Harris’s tiebreaking vote giving control to the Democrats.Mr. Biden’s sagging approval ratings — not just in Texas but even in Democratic strongholds like California — and the lingering cloud of the coronavirus on life, the economy and schools have emboldened many Republican voters, candidates and strategists.But Republicans fear nominating candidates outside the mainstream. The party suffered a series of stinging defeats in two otherwise favorable cycles in the recent past, 2014 and 2010, with candidates who repelled broad swaths of the political middle that still decides elections.A Guide to the Texas PrimaryThe 2022 midterm elections begin with the state’s primary on March 1.Governor’s Race: Gov. Greg Abbott’s rightward shift will face a test in November. His likely challenger, Beto O’Rourke, is haunted by his 2020 presidential bid.Attorney General’s Race: Whether Ken Paxton can survive the G.O.P. primary may be the biggest test yet of Donald Trump’s continued power over voters.A Changing Landscape: Issues like abortion and immigration are driving Hispanic voters in Democratic strongholds to switch parties and prompting liberal candidates to shift tactics.A Deepening Divide: Competitive districts are being systemically erased across the country. Texas is an especially extreme example.New Voting Law: Officials have rejected thousands of absentee ballots based on new requirements, an alarming jump ahead of the primary.The concern among Texas Republicans chiefly centers on the attorney general, Ken Paxton, who has attracted the attention of federal investigators after some of his own top aides accused him of corruption.Despite the hostile national climate, Democrats have scored some notable recruiting successes, including two high-profile candidates who came up just short in 2018: Beto O’Rourke, who is running for governor of Texas, and Stacey Abrams, who is running again for governor of Georgia.Beto O’Rourke campaigning for Texas governor in Tyler in early February.Montinique Monroe for The New York TimesMr. O’Rourke, whose Democratic nomination is mostly a formality, has been crisscrossing the state and raising money at a fast clip: $3 million in the last month. But Mr. Abbott, a prolific fund-raiser, outpaced him and entered the final days before the primary with $50 million on hand, compared to $6.8 million for Mr. O’Rourke.Texas has a two-step primary system: Any candidate who finishes below 50 percent will face off against the No. 2 vote-getter in a May runoff.Mr. Abbott appears to be leaving nothing to chance, spending $15 million in the last month alone and seeking to leave little daylight for his conservative opponents as he has overseen a sharp push to the far right in state government.Still, Mr. Abbott, who has Mr. Trump’s support, was booed in January at a Trump rally north of Houston, only winning over the crowd by invoking the president’s name more than two dozen times in his six-minute speech.“I think Greg Abbott has been in long enough,” said Anita Brown, 62, who attended a recent rally for a right-wing House candidate in The Woodlands, a suburban enclave north of Houston. “I would just like to have someone new.”Texas is where Mr. Trump suffered one of his rare primary endorsement defeats last year, in a House race, and while he has issued a range of endorsements, from governor down to Tarrant County District Attorney, he has mostly backed incumbents and heavy favorites.Bigger tests of his influence loom later in the spring and summer, in the Senate contests in North Carolina and Alabama, and in the governor’s race in Georgia. In that Georgia race, Mr. Trump recruited David Perdue, a former senator and governor, to attempt to unseat Gov. Brian Kemp, a Republican who refused to bend to Mr. Trump’s efforts to overturn the 2020 election.In Texas, Mr. Paxton, a regular guest on Fox News, commands the endorsement of Mr. Trump, but remains vulnerable because of his legal troubles: On top of his aides’ accusations of corruption, the Texas attorney general has been under indictment for securities fraud since 2015.His range of challengers represent the various Republican power centers vying to be the future of the party.There is George P. Bush, the son of Jeb Bush and a statewide office holder who has held himself out as the most electable conservative in the race, and Eva Guzman, a former state Supreme Court justice who has the backing of some traditional, business-aligned power players in Republican politics.Representative Louie Gohmert, a Trump ally whose speeches and remarks frequently land him on national television, is also running. He attended the Trump rally in Texas and got an unexpected shout-out, despite the former president’s endorsement of Mr. Paxton. Mr. Gohmert also posed with Mr. Trump during a photo line at the rally, but the Trump team refused to send Mr. Gohmert the picture, because they did not want him to use it in the primary, according to a person familiar with the exchange.Representative Louie Gohmert spoke at a forum in Midland with two other Republican candidates for attorney general, Eva Guzman, center, and George P. Bush, right.Tamir Kalifa for The New York TimesThe race has been multidimensional. Ms. Guzman has swiped at Mr. Bush, whose family dynasty has been weakened even among Texas Republicans. Mr. Bush has responded in kind. Mr. Paxton has traded attacks with Mr. Gohmert and, in recent days, started going after Ms. Guzman as well.“We haven’t seen a primary this consequential since the 1990s,” said Brandon Rottinghaus, a professor of political science at the University of Houston.The race is less about policy positions as it is about who holds power in the Republican Party now. “It will tell us a lot about Donald Trump’s juice in Texas,” Mr. Rottinghaus said.Mr. Paxton finished behind the rest of the Republican ticket in 2018, raising some fears that his renomination this year could provide a rare opening for Democrats in November. Republicans have won every statewide race in Texas since 1994.The national battle for power within the Republican Party is centered on the district of retiring Representative Kevin Brady, north of Houston, where a super PAC aligned with Representative Kevin McCarthy, the minority leader, has spent heavily to elect Morgan Luttrell, a Navy SEAL veteran. The activist wing of House Republicans has rallied behind Christian Collins, a former aide to Senator Ted Cruz.While the super PAC aligned with Mr. McCarthy is aiding Mr. Luttrell, the political arm of the House Freedom Caucus is boosting Mr. Collins.At a recent rally for Mr. Collins, Representatives Marjorie Taylor Greene of Georgia and Madison Cawthorn of North Carolina made clear that their support for Mr. Collins was about opposition to the existing political order in Washington.“This is primary season,” Ms. Greene said. “This is where we work out our differences. This is where iron sharpens iron.”On the Democratic side, two primaries pit the party’s ideological wings against each other.The race for one open seat features a socialist Austin city councilman, Greg Casar, taking on State Representative Eddie Rodriguez. The other race is in South Texas between Mr. Cuellar and a young progressive lawyer, Jessica Cisneros — a rematch in which abortion has been an issue for the district’s large number of Catholic voters.Both races have attracted attention from national progressive figures, including Representative Alexandria Ocasio-Cortez of New York and Senator Elizabeth Warren of Massachusetts — to the frustration of some Texas Democrats. They view the progressives’ efforts as potentially counterproductive for a party that has been losing ground among traditional Democratic voters in places like South Texas.“I get what people do on the fund-raising side,” said James Aldrete, a Democratic consultant. But unless Democrats do more to address the concerns of low-turnout voters, particularly in Hispanic communities, Mr. Aldrete added, “we’ll be in the same boat: no growth in the statehouse, no growth in the congressional delegation, no Democrat elected statewide.”When Ms. Ocasio-Cortez declared at a rally for Mr. Casar and Ms. Cisneros that “Texas turning blue is inevitable,” the clip was immediately picked up by Republicans, including Mr. Abbott, and wielded as an attack.“She was doing the work for Republicans,” said Matt Angle, a Democratic activist whose political action committee aims to unseat Republicans in Texas. He noted that Texas Democrats are more moderate in their approach to politics and more conservative in their views on issues like guns and abortion than national party leaders.“It’s a field trip for them,” Mr. Angle added. “For us, it’s the future of the state.” More