The Texas primaries on Tuesday will provide the first pieces of the puzzle that will be the 2022 midterm elections.

The ideological strength of the two parties’ factions. The tenacity with which Donald J. Trump maintains his hold on the Republican electorate. And, for bullish Republicans, the first indications of how favorable the political climate has become.

The full picture of the 2022 landscape will be revealed over the next six months through a series of state-by-state primaries. However, the country’s first primary elections in Texas provide a near-preview of many of the upcoming dynamics nationwide in an increasingly difficult environment for President Biden and the Democrats. This includes the impact of the Republican-controlled Texas Legislature’s strict new voting rules, as well as the political importance of abortion for both parties.

Last year, a Texas state law effectively prohibited most abortions after six weeks of pregnancy, and the United States Supreme Court is expected to rule this year in the Mississippi abortion case, which could affect procedures in multiple states. Progressives in South Texas are attempting to defeat one of the last anti-abortion Democrats still in Congress, Representative Henry Cuellar, and they received a political boost when the F.B.I. raided his home recently. Falling short under those conditions would be a setback for the left, especially after Mr. Cuellar narrowly won two years ago.

Gov. Greg Abbott, a Republican, is widely expected to defeat two spirited right-wing challengers at the top of the ticket. However, he is unlikely to receive anywhere near the 90% of the vote he received in his last primary four years ago, a testament to an increasingly restive Republican base.

Mr. Abbott has aggressively catered to that base in the last year and in the final days of the campaign, telling state agencies to investigate transgender adolescent treatment as “child abuse” and suggesting he might pardon more than a dozen Austin police officers indicted on charges of using excessive force during racial justice protests in 2020.

Texas lawmakers redrew the map in 2022, removing nearly all of the House seats that were competitive in the general election, emphasizing the importance of a handful of contested primaries in both parties. Republicans, in particular, are hoping to build on the party’s dramatic gains in South Texas and the Rio Grande Valley, particularly among working-class Latino voters, in the state’s lone open, tossup seat in 2020.

Republicans are energized across the country by the prospect of retaking both the House, which the Democrats control by a historically narrow margin, and the Senate, which is evenly divided with only Vice President Kamala Harris’ tiebreaking vote giving the Democrats control.

Mr. Biden’s dwindling approval ratings, not just in Texas but also in Democratic strongholds like California, and the lingering cloud of the coronavirus over life, the economy, and education have emboldened many Republican voters, candidates, and strategists.

Republicans, on the other hand, are wary of nominating candidates who are outside the mainstream. In two otherwise favorable cycles in recent history, 2014 and 2010, the party suffered a string of crushing defeats, with candidates who alienated large swaths of the political middle, which still decides elections.

The primary source of concern among Texas Republicans is the attorney general, Ken Paxton, who has drawn the attention of federal investigators after some of his own top aides accused him of corruption.

Mr. O’Rourke, whose Democratic nomination is largely a formality, has been touring the state and raising money at a rapid pace: $3 million in the last month. Mr. Abbott, a prolific fund-raiser, outpaced him and had $50 million on hand in the final days before the primary, compared to $6.8 million for Mr. O’Rourke.

Mr. Trump suffered one of his rare primary endorsement defeats in a House race in Texas last year, and while he has issued a variety of endorsements, from governor down to Tarrant County District Attorney, he has mostly backed incumbents and heavy favorites.

Greater tests of his clout will come later in the spring and summer, with Senate races in North Carolina and Alabama, as well as the governor’s race in Georgia. In that Georgia race, Mr. Trump enlisted former senator and governor David Perdue to challenge Gov. Brian Kemp, a Republican who refused to cave to Mr. Trump’s efforts to overturn the 2020 election.