Load the pot. Pour the water into the bottom of the Instant Pot, add the chopped potatoes, then rest the eggs on top of them so they sit above the water line and cook in steam.
Seal it up. Fit the lid, lock it into place, and turn the valve to the sealing position. If the valve is left venting, the pot will never come up to pressure.
Set the timer. Choose high pressure or manual and set the time to 4 minutes. The pot will take a few minutes to build pressure before that countdown begins.
Release and drain. As soon as the timer beeps, quick release the pressure. Lift the eggs into a bowl of cold water to halt their cooking and make peeling easier, then drain the water out of the pot.
Separate the eggs. Peel the hard-boiled eggs, split them, and drop the yolks into a mixing bowl. Set the whites aside for now, since they go in later as texture rather than as dressing.
Mash and mix the dressing. Break the yolks down with a fork until no lumps remain, then stir in the mayonnaise, buttermilk, mustard, a splash of pickle juice, and salt and pepper to taste. The dressing should look smooth and pourable, not stiff.
Dress the warm potatoes. Pour the dressing over the potatoes while they are still warm so it soaks in. Chop the egg whites and fold them in along with the celery, onion, and pickles.
Stir and chill. Mix until everything is evenly coated, cover the bowl, and refrigerate for a few hours so the flavours settle and the onion mellows.