New York City is requiring staff at city-run hospitals and clinics to get tested against COVID-19 on a weekly basis or get vaccinated, a move that prompted rallies by the nation’s largest healthcare union. Mayor Bill de Blasio announced the new policy at a press briefing on Wednesday, explaining the measure will go into effect on Aug. 2, and any employee who fails to show either a one-time proof of vaccination or a weekly negative test will have their pay suspended. “We see the delta variant, and we see the case numbers rising and it’s time to act. So, today we announce something new,” the mayor said. “We need a strong clear approach and every single one of our workers gets vaccinated or gets tested weekly.” The requirement marks the first time City Hall has mandated vaccinations or negative tests for public-sector workers. The Democratic mayor added that it is …