Efforts to question the legitimacy of the 2020 election in two swing states, nearly seven months after voting concluded, illustrate former President Donald J. Trump’s continued hold over the Republican Party and the staying power of his false election claims.

Georgia has already counted its presidential vote three times, with the same result: Mr. Trump lost. But a judge ruled last week that a group of voters must be allowed to view copies of all 147,000 absentee ballots cast in the state’s largest county.

The plaintiffs, led by a known conspiracy theorist, will have no access to the actual ballots, and the review will not change the outcome. But the ruling was a victory for a watchdog group that says it is looking for instances of ballot fraud, parroting Mr. Trump’s election lies.

At the same time, a Republican-led recount of more than two million ballots cast in Maricopa County, Ariz., resumed on Monday despite bipartisan denunciations of the effort as a political sham.

Even though Mr. Trump is not directly involved in the continued examinations of votes in Arizona and Georgia, his supporters’ widespread refusal to accept the reality of Mr. Biden’s victory has led Republicans to find new and inventive ways to delegitimize the 2020 results.