Donald Trump is facing increasing legal scrutiny in the crucial battleground state of Georgia over his attempt to sway the 2020 election there, and that heat is now overlapping with investigations in Congress looking at the former president’s efforts to subvert American democracy.

A criminal investigation into Trump’s 2 January call prodding Georgia’s secretary of state, Brad Raffensperger, to “just find” him 11,780 votes to block Joe Biden’s win in the state is making headway. The Georgia district attorney running the inquiry is now also sharing information with the House committee investigating the 6 January attack on the Capitol in Washington DC.

Meanwhile, a justice department taskforce investigating threats to election officials nationwide has launched inquiries in Georgia, where election officers and workers received death threats or warnings of violence, including some after Trump singled out one official publicly for not backing his baseless fraud claims.

Despite these investigations, Trump is still pushing bogus fraud claims in Georgia. Trump wrote to Raffensperger in September asking him to decertify the election results, which is impossible, and with an eye on the 2022 elections is trying to oust Raffensperger, as well as the state’s governor, Brian Kemp, and other top Republicans who defied his demands to block Biden’s win.

Former justice department officials and voting rights advocates say Trump’s conspiratorial attacks on Georgia’s election results, and the threats to public officials, need to be investigated diligently, and prosecuted if warranted by law enforcement, to protect election integrity and public officials.

Experts add that Trump’s alarming refusal to accept the Georgia election outcome and seek revenge on Republican officials who ignored his baseless fraud charges may affect a few pivotal 2022 races. His efforts may also encourage extremism and restrictions on minority and other voting rights similar to ones the Georgia legislature enacted this year.

Veteran DoJ officials and prosecutors say the criminal inquiry launched by the Fulton county district attorney, Fani Willis, into Trump’s call to Raffensperger and other efforts Trump made to overturn the Georgia results, seems well grounded, with ample public evidence. But they said it will probably take some time before Willis decides whether to bring charges.

Willis has said prosecutors are scrutinizing “potential violations of Georgia law prohibiting the solicitation of election fraud, the making of false statements to state and local governmental bodies, conspiracy, racketeering, violation of oath of office and any involvement in violence or threats related to the election’s administration”.

The Georgia investigation’s merits were bolstered in late September by the release of a well-documented 107-page study from the Brookings Institution detailing Trump’s high-pressure drive to block Biden’s win in the state. The report concluded that Trump faced “substantial risk of possible state charges predicated on multiple crimes”.

Boasting extensive documentation from the public record, the report notes that Trump’s broad effort to nullify the outcome in Georgia included personal contacts with the governor, the state attorney general and the secretary of state’s chief investigator.

“Trump engaged in a pattern of repeated personal communications aimed at altering the vote count and making himself the winner in Georgia,” Donald Ayer, one of several authors of the Brookings report and a former deputy attorney general in the George HW Bush administration, said in an interview.

“He did so in the absence of any even arguable evidence of voting or counting irregularities. Unless there are other presently unknown facts that would explain it, this conduct appears to satisfy the requirements of a number of Georgia criminal statutes.”

To further the Georgia inquiry, Willis reportedly has in recent weeks turned to the House select committee looking into the 6 January attack on the Capitol to share documents and information that could assist her work.

Willis’s outreach to the congressional committee doesn’t surprise some expert observers.

“Her resources to address local crime are already taxed and any investigative steps taken on Capitol Hill means her likely marathon of a case against the former president may be a little closer to the finish line,” Michael J Moore, a former Georgia prosecutor and Democrat, said in an interview.

The district attorney’s progress was underscored by Raffensperger telling the Daily Beast in August that Fulton county investigators had “asked us for documents, they’ve talked to some of our folks, and we’ll cooperate fully”.

According to the news outlet, at least four people in Raffensperger’s office have been interviewed, including attorney Ryan Germany and the chief operating officer, Gabriel Sterling.

On another legal front, the FBI has begun interviews in recent weeks with several Georgia election officials about death threats and other dangerous warnings they received in the months after the election from Trump backers suggesting falsely that Georgia officials were involved in election rigging.

For instance, Richard Barron, who heads the Fulton county board of elections, told the Guardian he was interviewed by two FBI agents in early September and informed them about two death threats he received, including one in the summer “full of white supremacist language” which warned he would be “served lead”.

“I hope the FBI makes some arrests,” Barron added. “People need to be held accountable for making threats against public officials.” Barron noted that threats against him and his majority Black staff rocketed after the election, when Democrats also won two Senate seats in the historically red-leaning state. Threats against Barron escalated further after Trump singled him out by name at a rally, he said.

Former justice department prosecutors say that the taskforce looking into these threats has to be aggressive. “Absent rigorous law enforcement, responsible citizens will shy away from seeking these types of important public jobs, especially if they feel their families will be under threat,” said Paul Pelletier, a former acting chief of the fraud section at DoJ.

But even with these inquiries heating up, Trump has continued to spread his false claims about the election results, as he did at a campaign-style rally in Perry, Georgia, on 25 September, where a few of his favored Georgia candidates spoke –including Representative Jody Hice, who is hoping to defeat Raffensperger in a primary contest.

Trump’s drive to retaliate against Republican politicians who defied his efforts to overturn Biden’s Georgia win has dismayed some veteran party operatives who see them as counterproductive.

“I think the Trump presence in Georgia has not been good for the GOP’s politics the last two years,” said Republican lobbyist Ed Rogers, who hails from Alabama. “Politics is about addition, and vengeance is not consistent with addition.”