The controversies surrounding convicted sex offender Jeffrey Epstein threaten to cast a long shadow over King Charles III’s upcoming visit to the U.S., his first American state visit since becoming monarch. The purpose of the king and Queen Camilla’s visit is primarily diplomatic, planned to commemorate the 250th anniversary of American independence. But as the monarchy continues to grapple with the  fallout  of Epstein-related disclosures, the royals’ visit could be overshadowed by questions about former Prince Andrew Mountbatten-Windsor and former United Kingdom Ambassador Peter Mandelson’s past ties to the disgraced financier. Their six-day visit is set to begin on Monday in Washington, with stops in New York City and Virginia to follow. Their  official itinerary  includes an   address to a joint session  of Congress delivered by Charles on Tuesday, followed by a state dinner hosted by President Trump and first lady Melania Trump at the White House, among other activities.…