This feeling — that the Republican base understands Trumpism and its best messengers better than G.O.P. leaders — is shaping the race in Georgia, as well as another Senate battleground contest this year in Arizona. There, Senator Martha McSally, a Republican, faces not only a energized Democratic electorate but a skeptical right-wing base. In both states, Republican governors appointed the senators, who now have to win their seats for themselves in November’s election.

In Georgia, many grass-roots conservatives are still bitter that Gov. Brian Kemp appointed Ms. Loeffler over Mr. Collins to the Senate in 2019 in what they say was a sop to the state’s Republican business and consultant class. They hope to soon right that wrong.

“I’m not opposed to the sitting senator, I’m just for Doug Collins,” said Lauren “Bubba” McDonald Jr., a member of the state’s public service commission whose local claim to fame was being the only statewide elected official to endorse Mr. Trump early in the 2016 Republican primary.