In a large mixing bowl, combine mayonnaise, Greek yogurt, Dijon mustard, lemon juice, honey, garlic powder, and onion powder. Whisk until smooth and well blended.
Add the shredded chicken to the dressing mixture. Use a spatula to gently fold until all chicken pieces are evenly coated.
Fold in the diced celery, grated carrot, minced red onion, and chopped parsley until vegetables are distributed throughout.
Season with salt and black pepper to taste. Start with 1/2 teaspoon salt and 1/4 teaspoon pepper, then adjust according to your preference.
Cover the bowl with plastic wrap or transfer to an airtight container. Refrigerate for at least 30 minutes to allow flavors to meld.
Before serving, give the chicken salad a final stir. Taste and adjust seasoning if needed. Serve on bread, over greens, or as desired.