Heat olive oil in a large pot over medium heat. Add onion, carrots, and celery; cook and stir until starting to brown, about 10 minutes. Stir in garlic; cook until fragrant, 1 to 2 minutes. Add turkey; season with salt, garlic powder, onion powder, oregano, and red pepper flakes. Cook and stir until turkey is starting to brown, 5 to 8 minutes.
Pour white wine into the pot and scrape any browned bits off the bottom with a wooden spoon. Stir in tomatoes, hot water, and ketchup. Simmer until flavors combine, about 30 minutes.