If using homemade sauce, prepare it now; otherwise have 1 1/4 cups store-bought sweet and sour sauce ready.
Trim the chicken breasts and cut into small bite-size cubes; pat dry with paper towels and season with kosher salt and freshly ground black pepper.
Pour oil into a large Dutch oven to a depth of about 1½ inches (about 2 quarts total) and attach a thermometer; heat to 350°F (175°C).
In a large bowl, whisk together the flour, cornstarch, baking powder, baking soda, 2 teaspoons kosher salt, and 1 teaspoon black pepper.
Add 1 1/4 cups water and the remaining 3 tablespoons oil to the dry ingredients and whisk until smooth to make the batter.
Toss the chicken cubes in the batter until fully coated.
Carefully lower battered chicken pieces into the hot oil a few at a time using a fork; fry at 350–375°F for 2–3 minutes per batch until golden and cooked through, stirring gently to prevent sticking.
Transfer fried chicken to a wire rack set over paper towels to drain and repeat until all chicken is cooked.
When frying is complete, remove the pot from heat and carefully pour off all but 1–2 tablespoons of oil into a heatproof bowl; return the pot to medium heat.
Add the red bell pepper, half the scallions, and the pineapple to the hot oil in the pot and cook, stirring, until the peppers are crisp-tender, about 2–3 minutes.
Pour in 1 cup of the sweet and sour sauce and cook until heated through, about 1 minute.
Add the fried chicken to the pot and gently stir to coat; heat just until the chicken is warmed through.
Serve immediately over cooked white rice, spoon extra sauce on the side, and garnish with the remaining scallions.