The state denies that the language creates quotas, saying that funding is not dependent on meeting the targets.
Cases among school staff, students remain low in the latest district update.
The previous program, which expired in November, transitioned hundreds of people into long-term housing.
Virtual students must test on campus but some schools are offering expanded options.
Shots are now available to people 16 or older with a wide range of preexisting conditions.
The reinstatement offer came after backlash from medical school students and alumni, as well as national media attention.
The city announced plans to scale back its testing efforts to focus on vaccinations. Its mass-vaccination plan was timed around the approval of a new vaccine from Johnson & Johnson.
NOLA Public Schools district expects 3,000 staffers to have gotten their first doses by the end of this week.
The action was part of a larger review of hundreds of non-unanimous verdicts.