Preheat oven to 400°F (200°C). Brush squash cut sides with 1 tbsp olive oil, season with salt and pepper, place cut-side down on a baking sheet.
Rub chicken with remaining oil, oregano, garlic powder, salt, and pepper. Nestle chicken on the same sheet beside the squash halves.
Roast 25 minutes, remove sheet, shred squash strands with a fork, spoon marinara into squash cavities and over chicken.
Sprinkle mozzarella over chicken and squash if using. Return to oven 8–12 minutes until chicken reaches 165°F and cheese melts.
Let rest 5 minutes, garnish, then serve strands scraped into bowls topped with chicken and extra sauce.