The center of the storm was about 20 miles northeast of Shreveport, La., on Sunday evening, and not going anywhere in a hurry. Most of southeast Louisiana remained under a flash flood watch until 7 p.m. Sunday because of how slowly Barry was moving, and flood watches were upgraded to warnings around Baton Rouge. The weather system was expected to move north through Arkansas Sunday night.

New Orleans appeared to have been spared the biblical deluge that forecasters thought it might get. The city’s total through Sunday night is now expected to top out at 6 inches or so; at one point there were forecasts that as much as 20 inches might fall. Tropical storm warnings and storm surge warnings for New Orleans have been canceled, and the city appeared to have avoided a painful stress test of the $20 billion flood protection system installed since the devastating flooding from Hurricane Katrina in 2005.

A group of volunteer search and rescue boaters, the United Cajun Navy, had a skeleton crew stationed near Baton Rouge on Sunday, according to the group’s founder, Todd Terrell, who lives in the city.

The group had been ready to launch their flatboats in flooded neighborhoods and rescue people from windows and rooftops. But on Sunday, he said, “we’ve been chasing nothing all day.”

Mr. Terrell said they used the day to practice animal rescues with the help of his dog. “We took it as a training day,” he said. “Everything’s winding down.”

Still, about 90,000 households and businesses had no power on Sunday evening, according to the tracking site PowerOutage.US. Mississippi and Alabama each had about 4,000, and there were 3,000 in Florida. Al Marmande, a member of the Terrebonne Parish Council, told a local TV station on Sunday that some residents of his coastal parish southwest of New Orleans could be without power for a number of days.

The state, parish governments, religious groups and the Red Cross had set up shelters across the state that could accommodate as many as 13,000 evacuees, but only about 500 Louisiana residents made use of them.

“Remember that while we were fortunate with Barry, we may not be so fortunate next time,” Collin Arnold, the homeland security director for New Orleans, said at a news conference in the afternoon. “We are entering the peak of hurricane season, so we need to remain ready.”

Marketa Walters allowed herself to breathe a much-needed sigh of relief on Sunday in Baton Rouge.

As secretary of the Louisiana Department of Children and Family Services, she was responsible for preparing emergency shelters throughout the state. Twelve hours earlier, the threat of widespread flooding was still very real.

“It was, go home and hunker down, because the storm is coming during the night,” Ms. Walters said. “But when I got up this morning and I’m looking around, and there’s nothing, I’m going, ‘Where is this storm?’”

When a weather briefing for state officials confirmed that the worst had passed, “it was only then I could begin to think, O.K., this is really over and I can go home and move the sandbags.”

Five miles down the road, Lisa Trahan, a deputy assistant secretary in the department, stood in the middle of the cavernous Raising Cane’s River Center, where nearly 3,000 people had taken refuge for several weeks during the floods in 2016.

Ms. Trahan, who managed the center through that emergency, watched on Sunday afternoon as her staff and National Guard troops broke down the 500 cots that had been set up, as a stack of new blankets, still in their factory wrappings, stood in the corner. She said it was a beautiful sight.

“I glad we didn’t have to unpack them,” she said of the blankets. “All of this goes to the warehouse until the next time. But it was a good trial run, because, you know, there are a few little waves off the African coast right now that could be trouble for us later.”

With the threat of storms, floods and evacuations always dangling over southern Louisiana, why don’t residents relocate permanently to higher, dryer ground?

“People love it here,” Ms. Walters said. “This is home, and they’re not going to leave. There is just something about this culture that is warm and welcoming and celebratory. The weather is just part of it, and you just get ready.”

There was only scattered light rain on Sunday morning in St. Mary Parish, which includes Morgan City, a small town about 20 miles from the southern coast of Louisiana where officials had been braced for a direct hit from the storm.

Officials there continued to express hope that the parish would be spared the worst, as it has been during several other recent Gulf storms.

“I think we’re in better shape than we were yesterday,” said David Naquin, the homeland security director for the parish. “If we just dodge the rain, we’ll be all right. We’ve got some rain coming today. We just don’t know how much we’re going to get.”

There had been no injuries or substantial structural damage in the parish by early Sunday, officials said. Even so, the authorities said they were forced to evacuate a small community outside Franklin, a town of about 9,000, because of what Mr. Naquin called “water issues.”

As evening descended in blacked-out Morgan City, residents seeking escape from hunger and cabin fever packed into one of the few open restaurants, a Waffle House a few miles from downtown.

“We’ve been slammed since 9 o’clock this morning,” said Tiffany Fontenot, a server. The food of choice? “Anything and everything,” she said.

The management there brought in a generator to stay in operation in a town that was 100 percent without power. As customers stood in line, most said life was still basically normal, except for the absence of lights and cooked meals.

“I ran out of food at the house,” said Anthony Landry, a 55-year-old truck driver. He added that he could always sleep in his truck if it got too uncomfortable in his house.

Barry never quite became the classic swirling figure seen with strong hurricanes, Christopher Bannan, a local National Weather Service meteorologist, said on Sunday morning.

The storm system was battered by dry air as it made landfall below Lafayette on the south-central Louisiana coast, Mr. Bannan said, which tamped down its rain bands, keeping them mostly confined to the Gulf of Mexico.

As the storm rotated, dry air over Alabama and Georgia was swept into the system, mixing with the moist tropical air in the Gulf, he said. A pair of competing high-pressure areas to the east and to the north created a phenomenon called wind shear — winds at different levels of the atmosphere moving in very different directions — and that slowed the storm to a crawl.

“When you have dry air and shear, a lot of the rain impacts are displaced from the center” of the storm, Mr. Bannan said. And that makes them hard to predict, he said: “Some of the computer models really struggle with weaker systems and their outer bands.”

Even so, he said, Barry’s outer storm bands could become “reinvigorated and take off” on Sunday if the area warms up. Flash flooding was still a risk, and a strong storm line was also moving toward Baton Rouge from Lafayette. A tornado warning was issued for Denham Springs, on the eastern edge of Baton Rouge, at 8 a.m.

“Still not out of the woods yet,” Mr. Bannan said.

Transit systems and airports in southeastern Louisiana were largely returning to normal operations by midday Sunday, after suspensions or disruptions at the height of the storm.

Only one or two delays on arriving or departing flights were reported at Louis Armstrong International Airport in New Orleans or at Baton Rouge Metropolitan Airport.

“I can’t tell you how excited I am,” Kim Fisher, whose flight from Louis Armstrong had been canceled on Saturday, told the NBC affiliate in New Orleans. “I just can’t wait to get back to Michigan. Yes, I can’t wait, can’t wait to get home.”

The Coast Guard reopened the Port of New Orleans on Sunday, and the Regional Transportation Authority said that its buses and most of its ferries would be back to full operation by 1 p.m., though not its streetcars.

“Streetcar service will continue to be replaced by bus service until the streetcar lines are cleared of debris and no cars are blocking tracks,” the agency said in a statement.

Three long-distance Amtrak trains that ordinarily reach New Orleans are operating only on the parts of their routes outside the reach of the storm on Sunday and Monday. Jason Abrams, an Amtrak spokesman, said the railroad would keep track of conditions and evaluate when to restore normal service.

Some churches and businesses in New Orleans were open Sunday morning, and runners and residents on some streets were out walking their dogs.

Moderate bands of showers with a few pockets of heavy downpours were moving slowly over Baton Rouge, the state capital, around midday Sunday, according to Mr. Bannon of the Weather Service.

The area was also under a tornado warning. One tornado was confirmed to have touched down in an eastern suburb, Denham Springs, around 8:15 a.m. Another possible tornado was spotted on the eastern edge of Baton Rouge around 10:20 a.m. Damage was reported, including a sighting of a trampoline hurled into the air.

Street flooding was reported in at least one area of the city, but to the relief of city officials, river levels in the area were holding steady.

“Most of the rivers are actually behaving now, because we did not get that 10 to 20 inches we were fearing,” Mr. Bannan said.

The predicted peaks of the Amite and Comite Rivers near the city were lowered well below previous estimates on Sunday, with neither now expected to approach flood stage.

The rain-swollen rivers were major contributors to the catastrophic flooding in and around Baton Rouge in August 2016. Thirteen people died in that disaster, and tens of thousands of residents were displaced; almost three years later, some have still not been able to return to their houses.

At the First Baptist Church in Denham Springs, La., about 290 congregants turned up for the 9:15 a.m. Sunday service. Ashley Green, who runs a women’s group at the church, said it usually draws 800 to 900 people.

“People are still afraid,” she said.

The service was interrupted at least twice by emergency alerts — loud siren-like tones emanating from cellphones throughout the congregation — followed by the gradually louder sound of rain beating down on the pitched roof.

The spacious church was built after the 2016 flood, when the congregation’s old building was inundated with up to 10 feet of water, reaching the sanctuary’s balcony.

Pastor Leo Miller spoke to the congregation about God’s purpose, even in tough times. He said he had grown physically weak on Thursday when he heard how high the nearby rivers were expected to rise.

“I know what 41 feet in the Amire River means,” said Mr. Miller, who wore khaki pants and a salmon-colored short-sleeved button-down as he led the service. His own house was flooded with 16 inches of water in 2016, he said, adding that those whose homes had flooded were given “a greater respect for that which will return.”

This time around, he said, he and his wife elevated their belongings above the 16-inch mark, stashed important papers in his truck, and packed a suitcase in case they needed to evacuate.

As the dire early crest predictions were later scaled back, he said, he wondered if divine intervention had played a hand: “Could it be that God heard the prayer of Denham Springs?”

Afterward, a woman shook his hand with a big smile and thanked him, one of several compliments he received from churchgoers. As she walked happily to her car in the light rain, Mr. Miller joked that the service “wasn’t that good — they’re just excited we didn’t flood.”

Correction: An earlier version of this briefing misspelled a National Weather Service meteorologist’s surname. He is Christopher Bannan, not Bannon.

Reporting was contributed by Richard Fausset and Beau Evans from New Orleans; Dave Montgomery from Morgan City, La.; Emily Lane and Richard Webster from Baton Rouge, La.; and Adeel Hassan and Nicholas Bogel-Burroughs from New York.