Set out and measure the mayonnaise, ketchup, butter, rice vinegar, sugar, garlic powder, onion powder, paprika, water, and salt. Let cold mayonnaise and ketchup sit out a few minutes so they whisk more easily.
Microwave 1 tablespoon of unsalted butter for 20 to 30 seconds until fully melted, then cool about 5 minutes until warm but not hot so it does not melt the mayonnaise.
Whisk 1 cup mayonnaise and 2 tablespoons ketchup in a medium bowl for about 30 seconds until smooth and evenly pink, scraping down the sides with a spatula.
Pour in the cooled melted butter, then add the rice vinegar, sugar, garlic powder, onion powder, sweet paprika, and salt. Whisk for about 1 minute until the sugar dissolves and the color is uniform.
Whisk in 2 tablespoons of water until the sauce loosens to a thick, pourable cream. For a thinner drizzle, add up to 1 more tablespoon of water, 1 teaspoon at a time, stopping when it looks slightly thinner than desired since it thickens as it chills.
Transfer the sauce to an airtight jar or a bowl with a tight lid and refrigerate for at least 1 hour so the seasonings soften and the flavors blend.
Stir the chilled sauce until smooth, taste it on a piece of rice or cooked vegetable, and adjust with a tiny pinch of salt, sugar, or a few drops of rice vinegar before serving in small bowls or a squeeze bottle.