NEW YORK—New York City will require all of its municipal workers—including teachers and police officers—to get coronavirus vaccines by mid-September or face weekly COVID-19 testing, Mayor Bill de Blasio announced Monday. The rule is expected to affect about 340,000 city employees, making the city one of the largest employers in the United States to take such action. While it isn’t a vaccine mandate—no workers will be forced to take a shot—officials hope the inconvenience and discomfort of weekly tests will persuade many to overcome a reluctance to get inoculated. The Sept. 13 deadline coincides with the start of public school, when the Democratic mayor has said he expects all pupils to be in classrooms full time. City health care workers and employees in congregate setting such as group homes will face earlier deadlines. Last week, the city had announced it was mandating vaccinations or weekly testing for workers in the …