WASHINGTON—The number of people seeking unemployment benefits fell sharply last week to 684,000, the fewest since the pandemic erupted a year ago and a sign that the economy is improving. The March 25 report from the Labor Department showed that jobless claims fell from 781,000 the week before. It’s the first time that weekly applications for jobless aid have fallen below 700,000 since mid-March of last year. Before the pandemic tore through the economy, applications had never topped that level. Still, a total of 18.9 million people are continuing to collect jobless benefits, up from 18.2 million in the previous week. Roughly one-third of those recipients are in extended federal aid programs, which means they’ve been unemployed for at least six months. Their prolonged joblessness could prove to be a long-term hindrance: Typically, many people who have been unemployed for extended periods struggle to find work even as the economy …