Under a sweeping new bill unveiled Friday, California would require businesses big and small to make sure all their workers, from employees to independent contractors, are vaccinated against COVID-19. The proposal, from a group of Democratic lawmakers, is part of a broader package of legislation aimed at limiting the spread of the deadly virus. “People are craving stability,” said Assemblymember Buffy Wicks, an Oakland Democrat who is one of the bill’s lead authors. “We can make that stability happen together.” The move comes after the U.S. Supreme Court blocked a nationwide vaccine mandate fo…