Preheat oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment paper.
Place squash, cut-side down, onto prepared baking sheet. Bake in the preheated oven until flesh is tender, 30 to 45 minutes. Cool until easily handled.
Scrape spaghetti squash flesh into a large bowl using a fork. Whisk eggs, evaporated milk, garlic powder, salt, and oregano together in a separate bowl; pour over squash. Mix chicken, ½ of the Parmesan cheese, ½ of the green
onions, bacon bits, and black pepper into the squash mixture and pour into a 9×13-inch casserole dish.
Top mixture with remaining Parmesan cheese and green onions and bake in the oven until done, about 45 minutes.