Over the past decade, Eric Coomer has helped make Dominion Voting Systems one of the largest providers of voting machines and software in the United States. He was accustomed to working long days during the postelection certification process, but November 2020 was different. President Trump was demanding recounts. His allies had spent months stoking fears of election fraud. And then, on Nov. 8, Sidney Powell, a lawyer representing the Trump campaign, appeared on Fox News and claimed, without evidence, that Dominion had an algorithm that switched votes from Trump to Joe Biden. This is the story of how the 2020 election upended Mr. Coomer’s life.