With the nation watching, the host on Iranian state television asked the question that so many people in Iran — from the political elite to people on the street — were wondering. “People are very worried about the supreme leader,” the host said to an official from Ayatollah Ali Khamenei’s office on Tuesday. “Can you tell us how he is?” He noted that viewers had sent a flood of messages asking the same thing. But the official, Mehdi Fazaeli, the head of Mr. Khamenei’s archives office, did not give a straight answer. Instead, Mr. Fazaeli said that he, too, had...