Cook the Potatoes and Eggs: Place a trivet in the bottom of the Instant Pot (or other electric pressure cooker) insert. Add 1 1/4 cups water. Place potatoes on the trivet. Place eggs on top of the potatoes. Set pressure cooking time for 4 minutes on high pressure.
While the potatoes and eggs cook, fill a small bowl with ice and water for cooling the eggs and lightly oil a rimmed baking sheet. When cooking time completes, vent the pressure using a quick release method. Using a slotted spoon, transfer the eggs to the ice bath.
Then spoon the potatoes onto the prepared baking sheet in one layer. Allow to cool. To cool overnight, cover with plastic wrap after the potatoes have stopped steaming and place in the refrigerator.
Make the Potato Salad: Peel and chop the eggs. Combine mayonnaise, onion, relish, olives, and mustard in a large bowl. Stir until blended. Add potatoes and eggs. Stir to combine. Add salt and pepper to taste. Spoon into serving dish. Sprinkle smoked paprika over the top. Serve chilled or at room temperature.