After an American fighter jet shot down the Chinese balloon that had floated across the United States, the reaction from Beijing — defensive, angered, yet hedging its options — illustrated the challenges facing China’s leader, Xi Jinping, as he tries to stabilize relations while giving little, if any, ground. Hours after the balloon was struck by a Sidewinder missile and crumpled into the waters off South Carolina, the Chinese Foreign Ministry declared its “strong discontent and protest” and dou