Place the diced potatoes in a large pot and cover with cold water. Add a pinch of salt. Bring to a boil over medium-high heat and cook until the potatoes are tender, about 10-15 minutes. Drain and let cool completely.
In a large mixing bowl, combine the mayonnaise, yellow mustard, apple cider vinegar, celery salt, garlic powder, onion powder, black pepper, and salt. Mix well until smooth.
Once the potatoes have cooled, gently fold them into the mayonnaise mixture until well coated.
Add the chopped hard-boiled eggs, diced celery, red onion, and sweet pickle relish to the potato mixture. Stir gently to combine all ingredients without mashing the potatoes.
Taste and adjust seasoning if necessary. If desired, fold in the fresh parsley for added color and flavor.
Cover the potato salad and refrigerate for at least 2 hours before serving to allow the flavors to meld.