WASHINGTON — The Trump administration paid El Salvador $4.76 million to detain up to 300 immigrant men for up to a year at a notorious mega-prison and barred the funds from being used to help asylum seekers, reproductive care or diversity initiatives, according to a court document filed Tuesday. It’s the first time the financial agreement has been made public after the White House initially said the deal amounted to $6 million. The payments were part of the Trump administration’s aggressive immigration crackdown and decision to invoke a wartime law to remove Venezuelan nationals. Some of those detained, including Kilmar Abrego Garica, of Maryland, whose mistaken deportation captured national attention, detailed psychological and physical torture. Instead, the planes landed in El Salvador.