Preheat the oven to 425°F and line a baking sheet with parchment paper.
Set up three shallow dishes. Place the flour in the first, beat the eggs in the second, and mix the panko with paprika, garlic powder, 1/2 tsp salt, and 1/4 tsp pepper in the third.
Pat the chicken tenders dry. Dredge each one in flour, dip in egg, then coat thoroughly with the seasoned panko. Arrange them on the prepared baking sheet and drizzle with olive oil.
Bake for 18 to 20 minutes, flipping once halfway through, until the coating is golden and the chicken reaches 165°F inside.
While the chicken bakes, combine the shredded cabbage and carrots in a large bowl. In a small bowl, whisk together the mayonnaise, apple cider vinegar, sugar, remaining 1/2 tsp salt, and remaining 1/4 tsp pepper. Pour the dressing over the vegetables and toss until evenly coated.
Serve the hot chicken tenders alongside the coleslaw.