WASHINGTON — Senate leaders and moderate Democratic Sen. Joe Manchin struck a deal late Friday over emergency jobless benefits, breaking a nine-hour logjam that had stalled the party’s showpiece $1.9 trillion COVID-19 relief bill. The compromise, announced by the West Virginia lawmaker and a Democratic aide, seemed to clear the way for the Senate to begin a climactic, marathon series of votes and, eventually, approval of the sweeping legislation. The overall bill, President Joe Biden’s foremost legislative priority, is aimed at battling the killer pandemic and nursing the staggered economy back to health.