Bring a large pot of generously salted water to a boil. Add the macaroni and cook 1–2 minutes past the package's al dente time, about 10 minutes total, so it stays tender once chilled. Drain and rinse under cold water until completely cool, then let it drip dry.
While the pasta cooks, whisk together the mayonnaise, mustard, apple cider vinegar, pickle relish and juice, sugar, salt, pepper, and paprika in a large bowl until smooth.
Add the drained macaroni, celery, bell pepper, red onion, and carrot to the bowl. Fold everything together until the pasta is evenly coated.
Cover and refrigerate for at least 1 hour (or overnight) to let the flavors meld. Before serving, stir well and taste — add a splash of milk or a spoonful of mayo if it looks dry, and adjust salt as needed.