Pour water in a multi-functional pressure cooker (such as Instant Pot(R)). Place steamer; add potatoes and eggs. Close and lock the lid. Select high pressure according to manufacturer's instructions and set timer for 4 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid.
Place potatoes in a large bowl. Peel eggs, remove egg yolks, and chop egg whites. Mash yolks and whisk with mayonnaise, vinegar, and mustard in a bowl until well combined to form the dressing.
Combine chopped egg whites, potatoes, and celery; pour in dressing and stir until evenly coated. Season with salt and pepper and sprinkle with chives. Refrigerate before serving.
