In a small bowl, whisk together mayonnaise, ketchup, garlic powder, paprika, and sugar if using. Add water gradually until smooth and desired consistency is reached. Refrigerate.
Heat a large skillet over medium-high heat. Melt butter and cook diced onion for 2 to 3 minutes. Add chilled rice and break apart clumps.
Push rice aside, scramble eggs, then mix into rice. Add soy sauce and sesame oil. Season and cook until heated through. Remove and set aside.
Sauté zucchini, sliced onion, and carrot in oil or butter for 4 to 5 minutes. Season and set aside.
Heat oil in skillet over high heat. Sear steak cubes 2 to 3 minutes per side. Add soy sauce in final minute. Rest briefly.
Melt butter in clean skillet. Add garlic and cook 30 seconds. Cook shrimp 1 to 2 minutes per side until pink. Add soy sauce and lemon juice if using.
Serve rice topped with steak, shrimp, vegetables, and creamy sauce. Garnish with green onions if desired.
