TOKYO—When Katie Ledecky finally saw that familiar number next to her name, the emotions flooded to the surface at the Tokyo Aquatics Centre. She tumbled over the lane rope to give her runner-up teammate a hug. She let out an uncharacteristic scream toward the American cheering section in the mostly empty arena. Finally, as the tears seemed ready to flow, she pulled the goggles back down over her eyes before exiting the pool. On her third try at these Olympics, Ledecky finally touched first. Bouncing back from the worst finish of her brilliant Olympic career, Ledecky claimed the first-ever gold medal in the women’s 1,500-meter freestyle Wednesday. About an hour earlier, she was blown away by Australia’s Terminator, Ariarne Titmus, who made it 2-for-2 in their rivalry with a victory in the 200 free. Ledecky didn’t even win a medal—the first time that’s ever happened to her in an Olympic …