Place potato chunks in a large pot and cover with cold water. Add 1 teaspoon salt and bring to a boil over high heat.
Reduce heat to medium and simmer potatoes for 15-20 minutes until tender when pierced with a fork but not falling apart.
Drain potatoes thoroughly and spread them on a baking sheet to cool for 10 minutes. This helps prevent a watery salad.
While potatoes cool, whisk together vegan mayonnaise, plant-based yogurt, nutritional yeast, Dijon mustard, apple cider vinegar, smoked paprika, and garlic powder in a large bowl.
Add cooled potatoes to the dressing along with vegan bacon bits, red onion, and parsley. Gently fold everything together until evenly coated.
Season with salt and black pepper to taste. For best flavor, cover and refrigerate for at least 30 minutes before serving.