Mix water, curry ketchup, tomato powder, Worcestershire sauce, coconut sugar, garlic powder, salt, and pepper together in a small bowl. Set aside.
Heat avocado oil in a large skillet over medium-high heat and add mushrooms and onions. Cook until vegetables begin to soften, about 5 minutes. Add turkey to skillet and cook over medium-high heat until the meat is no longer pink and begins to brown, 5 to 7 minutes. Stir in the tomato sauce mixture until well combined.
Reduce heat and simmer, covered, for 15 minutes. Remove the lid and simmer until the mixture thickens, about 5 minutes more. Place onto buns and serve.