To 6 or 8 quart Instant Pot, add 1 cup cold water, basket or trivet and place potatoes on top followed by eggs. Cook on High Pressure for 4 minutes.
Release pressure immediately by turning valve to Venting, open the lid and transfer eggs to an ice bath. Drain potatoes, then drizzle them with pickle juice and vinegar right in Instant Pot, and stir. Remove inner stainless steel pot from the Instant Pot and set aside to cool off.
In the meanwhile, chop pickles, celery and red onion. Add them to the pot with potatoes.
Peel the eggs, chop egg whites and mash egg yolks with a fork. Add both to the pot with potatoes along with yogurt, mayo, mustard, salt and pepper.
Stir gently until combined, cover and refrigerate for a few hours to allow flavors to blend. Serve cold.
Notes
To make ahead and store: It can be made and refrigerated for up to 2-3 days ahead. Do not freeze.
You don't have to peel red or yukon gold potatoes but you can. Don't cut smaller than 1 inch cubes or use Russet potatoes because they will fall apart.
Dijon mustard and any light color vinegar will work.