SAN ANTONIO — One recent Thursday, Ciara Brown, a junior at Fox Tech High School in San Antonio, stepped up to a small white table, pulled down her face mask and took a test that is still far from standard in American schools: a cotton swab up the nose.

“Testing is super-easy,” she said. “It’s not as scary as I thought it would be — it’s not a huge thing going up in your brain.”

The United States has struggled with Covid testing since the earliest days of the pandemic. Now, nearly two years in — and weeks into another Covid-disrupted school year — school systems across the nation are struggling with the role of testing in keeping children safe and in class.

Some, like Ciara’s in Texas, have gone all in; others offer no Covid testing at all. And still others say they want to do more testing but lack the resources or have been tripped up by obstacles and delays.

The numerous school districts in the San Antonio area reflect the nation’s political rifts. Some districts have adopted multiple precautions, including testing, to shield themselves from the virus. Some have few defenses.

Even as t​he worst of the early testing supply shortages have eased, and states have received federal money, including $10 billion from the American Rescue Plan, to implement school-based Covid testing programs​, many school districts are still floundering.

“There is just a lot more to testing than just swabbing a nose or spitting in a test tube,” said Dr. Laura Faherty, a pediatrician and researcher at the RAND Corporation who has studied school-based Covid testing.

A range of tests in Texas

School systems like Ms. Brown’s that have managed to establish large-scale testing programs are a case study in how much effort is involved.

San Antonio Independent School District offers weekly testing to every student and staff member, a commitment that requires proctors to collect nasal swabs on area campuses three days a week. A single collection event can take hours.

But the program, a partnership with the nonprofit Community Labs, is largely voluntary, and despite the district’s efforts, many families have not enrolled; about 30 percent of students are participating.

Ms. Brown, who has two immunocompromised family members, was eager to sign up. “I wouldn’t be able to live with myself knowing that if they got Covid it was because of me,” she said. “Knowing that I can keep them safe, myself safe, friends, even strangers safe is all that I really care about.”

But in the Boerne Independent School District, where masks are optional, testing is also optional and only available in the campus clinic by appointment.

While the district says that anyone who is sick should not come to school, symptomatic people will not be referred for testing or even sent home unless they are “unable to participate in instruction.”

Dr. Heather Riebel, a pediatric cardiologist who has treated Covid patients, said she has been “so careful” not to bring the virus home. Now, she worries her children may be more likely to contract it at school.

She has already pulled her fifth grader out of school once this fall, after he was exposed five times in one week to students infected with the virus. “It’s extremely disheartening,” Dr. Riebel said. (District officials did not respond to numerous interview requests.)

Elsewhere in San Antonio, the Northside Independent School District has taken a middle ground: rapid-testing students and staff members who are symptomatic, although students can only be tested if parents consent.

Superintendent Brian Woods has not ruled out the possibility of larger-scale screening if cases spike. But the district faces severe staffing shortages, making it difficult to scale up testing right now. “We’re not at that point yet,” he said.

The district is doing contact tracing, but the rollout has been bumpy. One elementary school can consult cafeteria cameras to help identify students’ close contacts. But they were not working on the day Andrea Ochoa’s 10-year-old daughter ate lunch with a student who later tested positive.

Ms. Ochoa, who has autoimmune issues, only found out about the exposure the following week, from her daughter.

“I’m not upset that a child got sick,” Ms. Ochoa said. “But I don’t want gossip between little kids to be the way us parents figure out how to advocate for our children.”

Policy patchwork

San Antonio is a microcosm of the patchwork of programs at schools across the country, even as the federal government invests more resources in testing.

“While some of the logistics are getting easier, there’s a pretty fragmented approach from school district to school district as to whether and how testing is being used,” Dr. Faherty said.

In Illinois, all public schools outside of Chicago are eligible for free SHIELD testing: weekly saliva tests developed by the University of Illinois at Urbana-Champaign.

But neighboring Iowa turned down the $95 million it was allocated for testing under the American Rescue Plan. The state’s department of education says other resources are available for schools; some districts are distributing take-home test kits, which are available at no cost from the state laboratory.

Even in states with coordinated programs, participation can be spotty. As of Sept. 21, just 24 percent of Virginia’s public school divisions had signed up for its federally funded testing program, which provides regular pooled P.C.R. testing and access to at-home test kits.

Elsewhere, the late-summer spike of cases has left schools scrambling.

“It’s a matter of playing catch-up,” said Dr. Richard Besser, president of the Robert Wood Johnson Foundation and the former acting director of the Centers for Disease Control and Prevention. “You can’t ask schools to implement broad-based testing protocols once the school year has already started, when there aren’t the supplies and the personnel and the logistics in place.”

Illinois’s SHIELD program was bombarded by last-minute sign-ups; as of Sept. 21, 43 percent of participating public schools opted in after Aug. 23, a SHIELD representative said.

The program takes three to six weeks to launch; several weeks into the school year, most participating schools have not yet started testing.

Chicago Public Schools has its own repeatedly-delayed program. The district initially said weekly screening would be available to every student when schools opened on Aug. 30. The district now says the program will be fully operational by the end of September, attributing the delay to the need to conduct background checks on the testing company’s employees.

Local parents have expressed frustration about shifting timelines and slow updates. “There is no clear line of communication,” said Debora Land, who has a high school sophomore in the district and is a parent representative on her local school council. “Parents have been asking, ‘What’s your plan, what’s your plan, what’s your plan?’”

As of Sept. 17, just 3 percent of students had enrolled in the testing program, the district said.

In New Orleans, the district has actively encouraged families to enroll in its weekly P.C.R. testing program — offering multilingual online sign-ups and enrolling in a state-run program that pays students to get Covid tests, said district spokesman Richard Rainey.

But local schools have had to weather both Delta and Ida, a Category 4 hurricane that knocked out the city’s power, temporarily closed public schools and suspended testing. “We pivoted quickly after the storm passed to restart the regimen within a week,” Mr. Rainey said.

It takes a village

The rising demand for testing has also strained supplies. In Fresno, Calif., the school district has been unable to replenish its stock of rapid antigen tests and has had to cut back on its testing of student athletes as a result.

But the biggest challenge many schools face is staffing. Berkeley Unified School District used state money to hire seven people to staff its Covid testing team — and then dipped into its own coffers to hire 14 more.

For many districts in lower-income communities, that kind of financial outlay may be impossible. “We need to make sure the resources are there, in particular, in the communities that have been hit the hardest,” Dr. Besser said.

Protocols that work when transmission rates are low can become unsustainable when rates rise. Alachua County, Fla., allows quarantined students to return to school early if they test negative for the virus on the fifth day of their quarantine.

During the worst of the August surge, nurses at some schools were testing as many as 40 to 50 quarantined students every morning.

Schools had to hope that no one needed medical attention during the hour or two it could take to test all those students, said superintendent Carlee Simon. “Like a kid doesn’t have an asthma attack or, you know, anybody needs an EpiPen.” She added: “Our nurses had a full-time job before Covid. Now Covid is a job.”

The workload has eased, but in the first month of school, 15 nurses quit.

In Grapevine, Texas, the school district’s testing center saw so much demand in early September that appointments were booked up days in advance. Amy Taldo, who runs the site, said she lacked the staff to expand. “I need an army,” she said.

And testing is only the first step. In San Antonio Independent, when students or employees test positive, a brigade of nurses conducts a laborious contact-tracing protocol.

To identify the close contacts of a single high school student, Lynn Carpenter, a district nurse, asks all their teachers for detailed seating charts. “I’ve got to know, are they at desks, are they at tables, how far apart are the tables?” she said.

If the student is an athlete, coaches get calls, too, with questions about practices and games.“It just kind of mushrooms out,” she said.

Ms. Carpenter, who works from a windowless, bare-walled office, sometimes needs several days to complete a single case. She has had calls with seriously ill staff members, some of whom broke down in tears. “It’s a heart-wrenching job,” she said.

A vaccine for children ages 5 to 11 could be authorized as soon as next month, further protecting elementary schools. But even then, it could be months until most young children are vaccinated — and many may never get the shots, Dr. Besser said.

So schools are forging ahead with what they have: limited staffing and limited time.

“I think it’s a very worthwhile thing that we’re doing,” Ms. Carpenter said. “I’m just looking forward to that day when this is behind us and I can go home.”