WASHINGTON—Texas’s costly Senate primary season is over. Now, Texas Attorney General Ken Paxton and State Rep. James Talarico are getting ready for the big fight—the general election. Buoyed by an endorsement from President Donald Trump, Paxton beat Sen. John Cornyn (R-Texas) in the May 26 runoff, ousting a multidecade incumbent who once chaired the National Republican Senatorial Committee, or NRSC, which backed him during the primary and runoff. As Texas enters monsoon season, the vast landscape is poised to soak up more than just rain. Cash will saturate the many media markets across a state that just went through the most expensive Senate primary in history, fueling appeals and attacks from the candidates and their allies ahead of November. Huge piles of conservative cash could help Paxton make up a fundraising gap in the race—one that yawned during his ultimately successful campaign against Cornyn....