It was one of those sticky images of Mr. Trump: the most powerful man in the world surrounded by a cavalcade of activity, the curve of a white feather poking out from a floral centerpiece, the blur of candles in candelabras and waiters in black vests affixed with royal-style crests. Next to the crests were bronze name tags that protruded awkwardly. Next to Mr. Trump was his multihyphenate secretary of state, Marco Rubio. In a photo, one could make out a smile and a bit of a laugh coming from Mr. Rubio’s mouth. Next to him was a woman in a 1920s-style headband who was looking out at the wide, lush expanse of Palm Beach.