Add the mayonnaise, sweet white onion, tomato ketchup, sweet pickle relish, lemon juice, paprika, kosher salt, and black pepper to a medium bowl, then whisk or stir until fully combined. The dressing should turn evenly pinkish-orange with the onion and relish distributed throughout and no streaks of mayo left behind.

Taste and adjust with more salt and black pepper if needed, then transfer the dressing to an airtight container and refrigerate it before serving. After at least 1 hour in the fridge, the texture thickens slightly, the onion mellows, and the flavor tastes more blended and balanced.