The city’s unease could prove pivotal next year, when Los Angeles will elect a new mayor in a contest that civic leaders say will have the highest stakes in decades.LOS ANGELES — Peter Nichols has lived for 22 years in a two-bedroom Cape Cod in the Fairfax District, in the flat, bungalow-lined midsection between the east and the west sides of Los Angeles. His block used to make him proud, with its neat lawns and palm trees: Crime was low. Streets were clean. When a problem arose — drug use in the park, traffic from the nearby Melrose Avenue shopping district — the city seemed to know how to address it.All that has changed.Homicides in his area have risen from one in 2019 to more than a dozen this year, according to the Los Angeles Police Department. He cannot drive more than a block or two without passing homeless encampments. Drought has withered the yards. Trash blows past on the Santa Ana winds.Waves of robberies have left armed guards posted for months outside high-end sneaker boutiques. Earlier this month, police officers responding to a burglary four miles from Mr. Nichols’s house arrested a parolee in connection with the slaying of an 81-year-old philanthropist in her mansion.“Now there’s this new variant,” he said about the coronavirus. “It’s like, what are we going to die of? Ricochet? Robbery gone wrong? Heat? Drought? Omicron? Delta? If you were watching this through the lens of a camera, you would think it was the makings of a disaster movie.”As the nation’s second-most-populated city struggles to emerge from the wreckage of the pandemic, a pileup of crises is confronting Los Angeles — and those who hope to become its next mayor next year.A Los Angeles police officer watching from a squad car as a homeless encampment is cleared in the Harbor City neighborhood of Los Angeles.Bing Guan/ReutersTens of thousands of people remain unhoused, violent crime is up and sweeping problems like income disparity and global warming are reaching critical mass. The anxiety is being felt in all corners and communities of the city. In a recent poll by the Los Angeles Business Council Institute and The Los Angeles Times, 57 percent of county voters listed public safety as a serious or very serious problem, up four percentage points from an almost identical poll in 2019.More than nine in 10 voters said homelessness was a serious or very serious problem. And more than a third said they had experienced homelessness in the past year or knew someone who had — a figure that rose to nearly half among Black voters.“Rome is burning,” former Mayor Antonio Villaraigosa recently said in a local television interview.In fact, crime rates are far below the historic peaks of the 1990s, coronavirus infections are a small fraction of last December’s terrifying levels and the city is making some progress in its breathtaking homelessness crisis, thanks to pandemic funding.But the unease is already shaping next year’s mayor’s race, a contest that civic leaders say will have the highest stakes in decades.“The problems we had before were big and they were complex, but they weren’t staggering and existential,” said Constance L. Rice, a civil rights lawyer, who sees mounting challenges from the pandemic, climate change and social injustice.“We’re in staggering-and-existential territory now.”The urgency comes as Los Angeles’s current mayor, Eric Garcetti, enters the homestretch of his administration. Ineligible for re-election because of a two-term limit, Mr. Garcetti is scheduled to leave office in December 2022.With roughly a year left on the job, he also is “between two worlds,” he said in an interview this fall: He has been tapped by President Biden to become the U.S. ambassador to India but it has taken six months for his confirmation even to be scheduled for its committee hearing on Tuesday. If confirmed, he could leave office early and the City Council could name an interim replacement, but the fate of his nomination is uncertain: Republicans have slowed approvals for scores of the president’s nominees, and additional hurdles have arisen involving City Hall.More than a dozen mayoral hopefuls are vying to replace Mayor Eric Garcetti, who is ineligible for re-election because of a two-term limit.Erin Schaff/The New York TimesFederal prosecutors have charged a former deputy mayor in a bribery scandal. A former member of the mayor’s security detail has sued the city, accusing a former top mayoral aide of sexual harassment. The former head of the city water and power department has agreed to plead guilty to bribery charges in a case involving the city attorney. And at least three City Council members have been convicted or indicted on public corruption charges.Even without those distractions, Mr. Garcetti can only do so much. Los Angeles’s mayor is weak compared with other big-city mayors. Shaped by backlash to the East Coast machine politics of the early 1900s, Los Angeles is famously ambivalent about power and institutionally diffuse.Only about a fifth of the 20 million people in greater Los Angeles actually live in the amoebalike city limits. Newcomers often assume they can vote in city elections, only to discover that they actually live in West Hollywood or unincorporated Los Angeles County.Major initiatives require buy-in from myriad independent players — homeowners’ associations, unions, school districts, county supervisors, nearly 90 surrounding cities. Yet Los Angeles mayors are often held responsible for vast quandaries like homelessness and port backups.Mr. Garcetti has been dogged for the past two years by assorted protests, and at one point demonstrators spray-painted and toilet papered the Tudor-style, city-owned mayoral mansion. But he has tirelessly urged Angelenos to maintain perspective. His tenure has had some notable successes: The city moved aggressively to deal with the pandemic, has passed major initiatives to fund transportation and affordable housing, is considered a national leader in climate policy and in 2028 will host the Olympics.At a news conference to announce a crackdown after a spate of flash mob robberies — in which large groups rush into a store and overwhelm employees — stunned the city, Mr. Garcetti reminded that Angelenos were statistically still in perhaps “the safest decade of our lifetimes.”In the interview in his City Hall office — an iconic room decorated with Frank Gehry chairs and Ed Ruscha paintings — he framed the past several months as a delayed societal response to the pandemic. “You come up for air and you kind of feel all the trauma that you’ve had to see and push down and witness and give voice to,” he said.White flags outside Griffith Observatory honoring the Los Angeles County residents who have died from Covid-19, one of the area’s many crises.Mario Tama/Getty ImagesMore than a dozen mayoral hopefuls are campaigning to succeed him. They include local politicians such as Mike Feuer, the city attorney, and Joe Buscaino, a former police officer now on the City Council, along with better-known figures such as Kevin de León, a councilman and former State Senate leader, and Representative Karen Bass, the former chair of the Congressional Black Caucus who was on Mr. Biden’s short list for vice president.Potentially in the mix, too, is the billionaire developer Rick Caruso, a former police commissioner and a onetime Republican. Shortly before Thanksgiving, Mr. Caruso’s own mall, the Grove, was stormed by a flash mob that smashed a Nordstrom display window with sledgehammers.Mr. Caruso, in television interviews, blamed the robbery on a $150 million cut to last year’s $1.7 billion-plus police budget and on lax prosecution, calling it “a manifestation of deciding we’re going to defund the cops.” (City leaders backed a modest increase in funding this year.)Rick Caruso has hired a team of political consultants to weigh his odds in a run for mayor of Los Angeles.Rozette Rago for The New York TimesMr. Caruso has not said he will run, but he has hired a team of top California political consultants to help determine his chances. But his remarks underscore the potential that the mayoral race will exacerbate the state’s long-running fight over criminal justice.In the calls for crackdowns, progressive activists hear a retreat from reforms won after the George Floyd protests and echoes of the tough-on-crime rhetoric in the 1990s that led to mass incarceration.“Folks like Rick Caruso have been waiting for an opportunity to put more money into policing,” said Melina Abdullah, a professor of Pan-African studies at California State University, Los Angeles, and a co-founder of the city’s chapter of Black Lives Matter. “I think we need to be wary of that. When we say, ‘Defund the police,’ it doesn’t mean we don’t want public safety. It means we want resources for communities.”Ms. Bass, who is considered the front-runner and would leave her congressional seat to become mayor, says that “first and foremost, people need to feel safe,.” But she said she also is reminded of the 1990s, when she was a physician assistant in South Los Angeles advocating for social programs in the midst of the crack epidemic.Representative Karen Bass is considered the front-runner in the mayoral race.Erin Schaff/The New York Times“People were angry because of the violence — the Crips and Bloods, the crack houses,” she recalled, sitting in her Baldwin Hills living room. Through the sliding glass door of the modest ranch house, the city unfurled to the horizon, interrupted only by the Hollywood Hills and the abrupt metallic bar chart of downtown.“That’s what is frightening to me now — the anger,” she said. “And my concern is the direction the anger can move the city in.”Other powerful currents could also propel voters between now and June, when they will winnow candidates down to a two-person November runoff unless one gets a majority. Under a new state law, every registered and active voter will be mailed a ballot. And this will be the first mayoral race since Los Angeles began aligning local elections with those at the state and national level, holding them in even-numbered years.The new system is expected to amplify turnout among Latino, Asian and younger voters — groups that have historically been underrepresented in local off-year elections. The electorate’s new mix could challenge the center-left alliances among businesses and Black and liberal Jewish voters that long have determined mayoral contests.Mr. de León, a son of Guatemalan immigrants who rose through organized labor to lead the California Senate from his longtime Eastside district, noted that, while none of those groups are monoliths, sheer demographic math could sway the election as much as any crisis. Over a breakfast taco in the downtown Arts District, the energetic progressive swiftly corrected an outdated statistic when asked if the city’s 40 percent Latino population might be an edge for a candidate with a Latino surname.“Forty-nine percent,” he said with a smile.Kevin De Leon, a City Council member and former State Senate leader running for mayor, said demography could sway the election.Jessica Pons for The New York TimesHe is deeply aware, however, of challenges that await the next mayor. Mr. de León’s Council district, which includes Skid Row, has more homeless people than the entire city of Houston, and he has set a citywide goal of creating 25,000 new housing units by 2025.“We simply can’t go back to the old normal,” he said. “All you have to do is look at the encampments in every neighborhood in Los Angeles. Families standing in line for blocks just to pick up a box of food to feed their children — the panic and anxiety.”On Melrose, Mr. Nichols, who runs a community group focused on public safety, will be watching. This year, for the first time in the 14 years since it was founded, his group is holding candidate forums. In recent weeks, he said, more than 200 people joined a Zoom call with aspiring City Council members, and mayoral candidates will be up next.“I couldn’t believe it,” he said. “People joined from all over the city. I expect a shake-up from the top down.” More