WASHINGTON—The number of Americans filing new claims for unemployment benefits rose slightly last week but continuing claims dropped, another indication that the labor market recovery from the COVID-19 pandemic continues to be choppy. Businesses have reopened at a rapid clip, boosted by a rollback in restrictions. Still, the job market rebound has been anything but steady despite recent employment gains. Initial claims for state unemployment benefits rose 2,000 to a seasonally adjusted 373,000 for the week ended July 3, the Labor Department said on Thursday. Economists polled by Reuters had forecast 350,000 applications for the latest week. “Through some of the noise in the data it still looks like the trend for filings keeps moving lower over time,” said Daniel Silver, an economist at JPMorgan in New York. Lack of affordable child care and fears of contracting the coronavirus have been cited for keeping workers, mostly women, at home. There …