Preheat oven to 400 degrees. Place parchment paper in a 9 x 13 baking sheet with 1 inch lip. In a skillet, heat olive oil and butter. Add onions and cook until soft and translucent. Add garlic and cook for several minutes. Add minced mushrooms and cook until mixture loses most of the moisture thickens up slightly. Transfer mixture to a large bowl. Add Worcestershire sauce and 3 tablespoons of ketchup. In a bowl, combine breadcrumbs, oats and milk. Stir to a paste-like consistency. Add the paste to the bowl with onion and mushrooms. Add eggs, water, ground turkey, salt, pepper, red pepper flakes and thyme. Gently mix until all ingredients are well combined. Spoon mixture onto the parchment lined baking sheet and form into a loaf shape. In a small bowl mix together the remaining 4 tablespoons of ketchup and Gochujang sauce. Spread over the top of the turkey loaf. Bake uncovered at 400 degrees for about 50 minutes. Let rest for 5 minutes before slicing.