Pour water into the pot of a multi-functional pressure cooker (such as an Instant Pot) and place a steamer basket inside. Place potatoes in the steamer basket. Arrange eggs on top of the potatoes.
Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 4 minutes. Allow 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. Use tongs to transfer eggs to an ice bath and let cool for 10 minutes.
Meanwhile, combine celery, mayonnaise, green onion, mustard, relish, and paprika in a large bowl. Stir until evenly combined.
Peel and chop the eggs. Stir eggs and potatoes into the dressing. Season with salt and pepper. Cover and refrigerate for 1 hour before serving.