Government leaker and transgender rights advocate Chelsea Manning entered the U.S. Senate race in Maryland to huge fanfare this year, but her campaign is poised to wind down quietly Tuesday when voters head to the polls on primary day. Ms. Manning promised to shake up the race, using her high profile to push a platform that included creating a universal health care system, abolishing federal law enforcement agencies such as U.S. Immigration and Customs Enforcement, and combating what she called the American “police state.” But the strain of being in the public eye after seven years in prison for leaking...