Place a large rimmed baking sheet in the oven; preheat to 425 degrees F.
Combine chili powder, cumin, 1/2 tsp. salt, garlic powder, paprika, and ground pepper in a large bowl. Transfer 1 tsp. of the spice mixture to a medium bowl and set aside. Whisk 1 Tbsp. oil into the remaining spice mixture in the large bowl. Add chicken, and vegetables; toss to coat.
Remove the pan from the oven; coat with cooking spray. Spread the chicken mixture in an even layer on the pan. Roast for 15 minutes.
Meanwhile, combine black beans with the remaining 1/4 tsp. salt and 1 Tbsp. Chili oil in a large bowl; toss to coat.
Remove the pan from the oven. Stir the chicken and vegetables. Spread beans evenly over the top. Roast until the chicken is cooked through and the vegetables are tender, 5 to 7 minutes more.
Meanwhile, add yogurt, Calamansi, and water to the reserved spice mixture; stir to combine.
Divide the chicken and vegetable mixture among 4 bowls or in a tortilla. Drizzle with the yogurt dressing and serve.