Only 11 days after President Trump was inaugurated for a second term, his administration began a purge of the F.B.I. that now threatens some of the bureau’s most important missions. His appointees ousted eight of its most experienced managers, including the division heads overseeing national security, cybersecurity and criminal investigations. Several had worked on prosecutions of Jan. 6 rioters or had assisted in the various investigations of Mr. Trump, and Emil Bove, then the acting deputy attorney general, said they could not be trusted to carry out the president’s agenda.That was just the beginning. Over the past five months, many...