After a wakeful night confined to a Mecca palace lounge, Saudi Arabian Crown Prince Mohammed bin Nayef emerged into a marble-walled room the morning of June 21. The 57-year-old prince found a waiting crowd, cameras, a security guard with his hand on a gun—and his cousin Mohammed bin Salman, 31, the favored son of King Salman, newly installed as his successor as heir apparent and crown prince. An inside…