While the Biden administration has accelerated processing after Trump-era restrictions and a pandemic slowdown, visa backlogs remain large.The flow of immigrants and refugees into the United States has ramped up over the past year, helping to replenish the American labor force after a decline that began with restrictions imposed under the Trump administration and that was compounded by the pandemic.The Biden administration has been accelerating visa processing and broadly using humanitarian parole programs for migrants fleeing war and economic instability. Those efforts have driven a rebound in the foreign-born population — welcome news for the Federal Reserve, which has been concerned that a persistent shortage of workers could send wages higher and lead inflation to become entrenched.Friday’s employment report for January, showing a blockbuster gain of 517,000 jobs, confirms that the economy continues to demand more labor. Moderating wage growth, however, suggests that enough workers are arriving to keep costs in check.“When the unemployment rate goes down, you would normally expect wage inflation to go up, but that’s not what’s happening,” said Torsten Slok, chief economist at Apollo Global Management. “So there must be something else moving in the labor force, and there is a very likely explanation here that immigrants are coming in and taking jobs.”But despite the resurgence in the foreign-born labor force — about four-fifths of it are people legally allowed to work in the United States, by one calculation — there are bottlenecks.Legal immigration remains below pre-Trump levels. Hundreds of thousands of people await interviews with U.S. consular officials to obtain immigrant visas. Millions of asylum cases are pending, and getting work authorization for those already here can take years.The uneasy state of immigration policy, a contentious political issue for years, is felt every day by Al Flores, the general counsel at a group of Tex-Mex restaurants in the Houston area and a restaurant owner himself.When the restaurants reduced staffing during the pandemic, many of their workers went to places that were hiring — like the construction industry — and rehiring was a challenge given the sharp immigration slowdown of 2020.The company now employs about 2,500 people, at least 12 percent of whom are able to work under the Deferred Action for Childhood Arrivals program, or DACA, which has been in jeopardy since Mr. Trump decided to terminate it; challenges are winding their way through the courts. Another 10 percent have temporary protected status, a designation granted to people who have fled from countries in turmoil, which often allows them to stay in the United States for years.Alma Moreno, a cook at Hacienda Tacos y Tamales in Houston, is a Salvadoran who has temporary protected status in the United States.Callaghan O’Hare for The New York Times“It’s gotten a little bit better, but we’re seeing a drop in permanent visas and an increase in temporary ones,” Mr. Flores said. “At some point those folks have to move on, sometimes to other countries where there’s more open arms. And that’s tough for us, because we need the labor.”The State of Jobs in the United StatesEconomists have been surprised by recent strength in the labor market, as the Federal Reserve tries to engineer a slowdown and tame inflation.Job Trends: The Labor Department reported that the nation’s demand for labor only got stronger in December, as job openings rose to 11 million.Burrito Season: Chipotle Mexican Grill, the fast-casual food chain, said that it planned to hire 15,000 workers ahead of its busiest time of year, from March to May.Retail Industry: With consumers worried about inflation in the prices of day-to-day necessities like food, retailers are playing defense and reducing their work forces.Tech Layoffs: The industry’s recent job cuts have been an awakening for a generation of workers who have never experienced a cyclical crash.The path of immigration policy will have a substantial bearing on the nation’s supply of workers, which has been expanding more slowly as native-born workers have fewer children. The Congressional Budget Office projects that by 2042, net immigration will be the nation’s only source of population growth.The dip in immigration occurred in multiple ways, beginning with the inauguration of Donald J. Trump as president in 2017. The cap on refugees allowed to enter the United States dropped to 15,000 in 2020, the lowest level in decades. Measures like a ban on immigrants from Muslim countries, even though the courts eventually overturned it, deterred people from trying to come.Some of Mr. Trump’s changes were more subtle. The Department of Homeland Security slow-walked visas by asking for more evidence and interviews, said Shev Dalal-Dheini, head of government affairs for the American Immigration Lawyers Association, and then it shut down processing — which is largely paper-based, not electronic — during the pandemic.Even when lockdowns eased, U.S. Citizenship and Immigration Services had a difficult time ramping back up because with no processing fees, it lacked the funds to rehire staff who had left. Staffing at U.S. embassies, which conduct visa interviews in other countries, had also atrophied.“They’ve had to play catch-up with that for a long, long time,” said Ms. Dalal-Dheini, who left the immigration agency in 2019. “Once the Biden administration came in, they reset some of those policies designed to slow down the process, and then were focused on building back up their work force.”The result has been that visas for visitors, temporary workers and permanent immigrants rose to 7.3 million in 2022, up from 3.1 million the previous year but still down from the more than 10 million issued annually in the three years before Mr. Trump took office. President Biden also granted humanitarian parole and temporary protected status to migrants from several more countries, including Ukraine and Afghanistan, allowing hundreds of thousands more people to stay and the opportunity to work in the United States.The number of new citizens hit a 15-year high in 2022. And the cap on refugees was raised to 125,000 in 2022, although the administration managed to process only about 25,000.Those measures increased net immigration to about a million people last year, the highest level since 2017, according to the Census Bureau. The foreign-born work force grew much more quickly than the U.S.-born work force, Labor Department figures show. (According to an analysis by FWD.us, a business-backed group that favors more immigration, 78 percent of the foreign-born labor force has legal work status.)The growth in immigration has helped power the job recoveries in leisure and hospitality and in construction, where immigrants make up a higher share of employment, and where there were bigger increases in wages and job vacancies. More