Place whole potatoes in a large pot and cover with cold water by 2.5 cm (1 inch). Add 1 tsp salt. Bring to a gentle boil over medium-high heat, then reduce to a simmer for 12-15 minutes until a knife slides in with slight resistance.
Meanwhile, mix Hellmann's mayonnaise, yellow mustard, apple cider vinegar, celery salt, and black pepper in a bowl. Taste and adjust acidity; the dressing should be bright but not sharp.
Drain potatoes in a colander and let sit 5 minutes to steam off excess moisture. While warm, peel if desired and cut into 2 cm (3/4 inch) chunks so edges remain intact and creamy centers stay fluffy.
Fold warm potato chunks into the dressing gently so the mayo coats without turning gluey. Warm potatoes absorb flavor; you should see a glossy coating and feel a plush texture when pressing a piece between fingers.
Fold in chopped celery, red onion, and chopped eggs. The celery gives a lively crunch, onion adds bite, and eggs add richness and body. Adjust salt and pepper to taste.
Chill for at least 1 hour to let flavors marry. Before serving, stir in fresh parsley for herb aroma and a final drizzle of vinegar if it needs brightening. Serve cool, not ice cold, to let flavors bloom.