WASHINGTON—U.S. private payrolls increased more than expected in September as COVID-19 infections started subsiding, boosting hiring at restaurants and other high-contact businesses. Private payrolls increased by 568,000 jobs last month, the ADP National Employment Report showed on Wednesday. Data for August was revised lower to show 340,000 jobs added instead of the initially reported 374,000. Economists polled by Reuters had forecast private payrolls would increase by 428,000 jobs. “Stronger job growth in September could indicate that the drag on hiring from the recent increase in coronavirus cases is fading,” said Gus Faucher, chief economist at PNC Financial in Pittsburgh, Pennsylvania.Employment gains averaged 410,000 jobs in the third quarter, a slowdown compared to the second-quarter average of 748,000. Last month, the leisure and hospitality industry added 226,000 jobs after creating 155,000 positions in August. Manufacturing payrolls increased by 49,000 jobs, while hiring at construction sites also rose by 49,000. Job gains …