Preheat oven to 400 degrees. Line two rimmed baking sheets with tinfoil and spray with cooking spray.
Add vegetables to the prepared sheet pans (keeping one pan less full, so that you'll have room to move them to one side and add the chicken later). Drizzle veggies with olive oil and season them with seasoned salt, Italian seasoning, smoked paprika, and black pepper, then toss to coat. Spread veggies out in a single layer and bake at 400 degrees for 15 minutes.
Meanwhile, trim the chicken tenders and toss them in a bowl with olive oil, seasoned salt, garlic powder, cayenne, smoked paprika, and black pepper until well coated with the spice mixture.
Remove pans from the oven. Stir veggies and flip over the zucchini, then push the vegetables on your less full baking sheet over to the side in order to make room for the seasoned chicken tenders (but leave veggies in a single layer). Arrange the chicken in a single layer on the pan, then sprinkle both pans of chicken and vegetables with shredded Parmesan.
Return to oven, switching pans between their original racks, and roast for another 12-15 minutes or until chicken is cooked through to 165 degrees internal temperature.
Notes
Cooking time will vary somewhat, depending on the thickness of your chicken tenders.