In January 2017, after Joe Biden swore in Kamala Harris as a U.S. senator, they posed for a traditional photo with Harris’s family. Harris, however, wasn’t done yet. She asked Biden if they could take another picture, but this time with her “extended family” — a dozen more friends and loved ones.

One of the people who came forward was Laurene Powell Jobs, one of the richest women in the world, with a fortune of over $11 billion. She stood just behind Biden’s shoulder in the picture, alon...