Line a 13x18-inch rimmed baking sheet with aluminum foil and drizzle with 3 tablespoons olive oil. Place the pan in the oven while it preheats. Preheat the oven to 425 degrees F (220 degrees C).

Stir together flour, onion powder, salt, garlic powder, paprika, and pepper in a shallow dish. Place beaten eggs in second shallow dish. Combine French-fried onions and breadcrumbs in a third shallow dish.

Dip each chicken tender first into the flour mixture, then the egg mixture, and finally the onion–breadcrumb mixture until fully coated; set aside.

Carefully remove the baking sheet from the oven and swirl to coat with the hot oil. Arrange coated chicken pieces onto the prepared baking sheet.

Bake in the preheated oven for 8 minutes. Flip and continue baking until the chicken is golden brown and cooked through, about 5 to 6 minutes more, or until an instant-read thermometer inserted into the thickest part reads at least 165 degrees F (74 degrees C).

Meanwhile, whisk together mayonnaise, sour cream, horseradish sauce, ketchup, white vinegar, onion powder, garlic powder, smoked paprika, salt, pepper, and cayenne for the dipping sauce in a bowl until smooth.

Serve chicken with onion dipping sauce.