Add water and chopped potatoes to the bottom of the instant pot. Place the eggs on top of the potatoes.
Secure the instant pot lid and turn the valve to sealing.
Select high pressure/manual and set timer to 4 minutes.
When the timer beeps, quick release the pressure. Remove the eggs to a bowl of cold water and drain the water from the pot.
Separate egg yolks from the whites of the hard-boiled eggs and place the yolks in a bowl.
Mash the yolks with a fork and then stir in the mayonnaise, buttermilk, mustard, a splash of pickle juice, and salt and pepper, to taste.
Pour the dressing over the warm potatoes. Chop the egg whites and add them to the potatoes along with the celery, onion, and pickles.
Stir well, cover, and refrigerate for a few hours to allow the flavors to blend.