President Biden’s decisive victory in the New Hampshire Democratic presidential primary provided him with a dose of good political news amid a season of Democratic anxiety about his campaign.

The symbolic, if largely expected, win on the strength of a write-in campaign comes as Mr. Biden and his party now shift more fully into general-election mode after former President Donald J. Trump triumphed in the state’s Republican primary on Tuesday. He beat Nikki Haley, the former governor of South Carolina, though she has vowed to continue her uphill battle against him.

“It is now clear that Donald Trump will be the Republican nominee,” Mr. Biden said in a statement, in which he thanked voters who wrote in his name. “And my message to the country is the stakes could not be higher.”

Mr. Biden is expected to campaign this weekend in South Carolina, which he and the Democratic National Committee selected to supplant New Hampshire as the first-in-the-nation primary.

He declined to appear on the ballot in New Hampshire after the Granite State refused to accept its demotion. But his allies in the state eventually stepped in, and the write-in effort, supported by top Democrats there, generated the kind of grass-roots energy for Mr. Biden that has not yet materialized in other states — and that he did not enjoy in New Hampshire’s primary in 2020, when he came in fifth place.

Kathy Sullivan, a former chairwoman of the New Hampshire Democratic Party who led a write-in Biden super PAC, said that a strong Biden showing in the state was important “to counteract the narrative that’s out there that he’s not popular” and to signal that he had the support of the Democratic base.

The decisiveness of Mr. Biden’s write-in victory over the long-shot challenger Dean Phillips, a Minnesota congressman who was one of 21 Democrats on the ballot, made the state’s insistence on voting first even more meaningful, she added.

“We go into the general election now,” she said.

But before the general election officially arrives, Mr. Biden will participate in the Democratic primary contests next month in South Carolina, Nevada and Michigan. Those races will test the Biden campaign’s ability tomobilize its most loyal voters, as polling has shown signs of weakness with core base constituencies. He is expected to address a gathering of South Carolina Democrats on Saturday.

In New Hampshire, Mr. Biden’s absence on the ballot left him exposed to a collection of opponents who had virtually no shot of winning the nomination but who saw an opportunity to win attention.

That group was led by Mr. Phillips, who pushed a message of generational change, denounced Mr. Biden, 81, as “unelectable,” and spent heavily on advertising as he highlighted the president’s snub of the state. One of his ads featured Bigfoot searching for Mr. Biden.

Mr. Phillips sought to tap into Democratic discontent with the president, which was evident on the ground.

“There should be a benchmark of 65, 68, 70 for being president,” said Richard Valley, 53, who lives in Manchester and voted for Mr. Phillips, who is 55 years old. “You need to be agile. You need to be in tune. You need to be at a higher level. You’re the leader of the free world!”

Mr. Biden’s allies argue that when Americans focus more squarely on the election, especially on the prospect of another matchup against Mr. Trump, disillusioned Democrats will rally around the presumptive nominee.

One such Democrat is Tiffani Cardinale from Concord, N.H. “To be honest with you, Joe Biden is not my favorite president,” she said. “But I’m very scared of what the alternative could be.”

She said that she cast a write-in vote for Mr. Biden in the primary, adding that she was concerned about the state of American democracy.

On Tuesday night, Mr. Phillips congratulated Mr. Biden at his watch party in Manchester, saying that the president “absolutely won tonight” — but, he added, “by no means in a way that a strong incumbent president should.”

Amid concerns from Democrats about the Biden campaign’s structure — and as his team gears up for a bruising general election swiftly coming into view — the president approved a leadership shake-up on Tuesday that will see two top White House aides take over functional control of the re-election effort.

The drama over this year’s nominating calendar began in late 2022, when Mr. Biden and the D.N.C. decided to reorder it, saying that Democrats should give states with more racial diversity greater influence. Their plan put South Carolina — the state that revived Mr. Biden’s flagging 2020 campaign — first and would have pushed New Hampshire to second, alongside Nevada.

But New Hampshire Democrats, who pride themselves on the state’s longtime first-in-the-nation tradition — a matter of state law — balked, and the state was stripped of its delegates.

Ultimately, leading Democrats in the state put aside their vociferous criticism of the calendar overhaul to back the head of their party, even as they staunchly defended their primary tradition.

“It’s in our D.N.A. — it’s part of who we are,” former Gov. John Lynch said. “But also, I think there are Democrats, myself included, who are willing to sort of step back and say, you know, What’s the bigger picture?”

Ms. Sullivan, a leader of the write-in campaign, said that there were important lessons from that effort that the national party could learn, especially when it comes to empowering grass-roots supporters.

Asked if she intended to share those conclusions with the Biden campaign, she replied, “If they’re interested in talking to us.”

“We’re here if they want to talk,” she laughed.

Nick Corasaniti and Anjali Huynh contributed reporting from Manchester, N.H., and Chris Cameron contributed reporting from Concord, N.H.