What’s alarming to national Republicans is that the awkwardness in Georgia may only offer a preview of what the party might confront during the post-Trump era, which itself may be a misnomer.

With Mr. Trump signaling that he intends to try to keep control of the party and potentially seek the White House again in 2024, G.O.P. lawmakers and operatives are bracing for a period in which they’re effectively handcuffed to a former president who demands veto power in intraparty elections.

“It’s very possible, if not likely, that Trump will be in a kingmaker position for the 2022 primaries,” said Todd Harris, a longtime Republican ad-maker. “Whether people like it or not, this is Trump’s party. And nothing that happened on Election Day or since then has done anything to change that.”

While some Republicans, especially in the country’s reddest precincts, are delighted about the prospect of Mr. Trump running the party from tropical exile at Mar-a-Lago, those who represent voters exhausted by the soon-to-be-former president are eager to move on.