Make the jerk sauce: whisk together the ketchup, 1/2 cup plus 1 tablespoon soy sauce, orange juice, vinegar, molasses, curry powder, cayenne, grated ginger, and 1 clove minced garlic in a bowl.
Marinate the chicken: toss the chicken tenders with about 1/4 cup of the sauce in a medium bowl; refrigerate 20–30 minutes and reserve the remaining sauce.
Grill the pineapple: while chicken marinates, grill or broil the pineapple sticks until charred on both sides; let cool and chop into chunks for the salsa.
Cook the chicken: heat 1 tablespoon peanut oil in a large skillet over high heat. Add the chicken with some of its marinade and cook about 2 minutes per side until nicely caramelized and cooked through; remove from the pan.
Stir-fry the peppers: add 1 tablespoon peanut oil to the hot pan, add the sliced red, orange, and banana peppers, and stir-fry 2–3 minutes until slightly softened; remove and set aside.
Fry the rice: add the last tablespoon of peanut oil to the pan, add the cold cooked rice and stir-fry about 4 minutes until heated through.
Season the rice: stir in 1 tablespoon soy sauce and about 1 tablespoon of the reserved jerk sauce, then add the cooked peppers back into the rice and toss to combine.
Make the pineapple salsa: in a bowl toss the grilled pineapple chunks with the finely chopped red onion, sliced cherry tomatoes, diced jalapeño, grated garlic, grated ginger, lime juice, and a pinch of salt; taste and adjust seasoning.
Serve: plate a portion of the pepper fried rice, top with the cooked jerk chicken, drizzle with any remaining reserved sauce if desired, and spoon the grilled pineapple salsa over the chicken.