Preheat the oven to 425 degrees F (220 degrees C).
Drain pineapple tidbits and place juice into a 1-cup liquid measure. Place drained pineapple in a large mixing bowl; set aside.
Add bell peppers, carrot, and onion to the pineapple tidbits. Pour 2 tablespoons avocado oil over top and sprinkle with salt and pepper. Stir until coated with oil and seasoning, then spread in a single layer on a sheet pan. Place chicken into the same bowl, drizzle with remaining 1 tablespoon oil, and season with salt and pepper. Toss to coat and nestle chicken pieces on the sheet pan between the pineapple and vegetable pieces.
Bake in the preheated oven until vegetables are tender and chicken is cooked through, about 25 minutes.
Meanwhile, add enough water to the reserved pineapple juice to make 1 cup liquid. Transfer 3 tablespoons of the liquid to a small bowl and add cornstarch. Stir with a fork or whisk until smooth.
Pour remaining liquid into a saucepan with brown sugar, rice vinegar, ketchup, soy sauce, chile-garlic sauce, ginger-garlic paste, and white pepper. Bring to a boil, stirring occasionally, over medium-high heat. Slowly add cornstarch mixture, whisking briskly. Return to a boil and allow to thicken, whisking constantly, about 1 minute.
Drizzle chicken, pineapple, and vegetables with sauce to serve.
You can use any neutral-flavored cooking oil for avocado oil.
To save time, instead of making the sauce, you may also use canned Asian sweet and sour sauce.
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