Bring a large pot of salted water to a boil. Cook chickpea pasta for 1 minute less than the package directions (about 7 minutes if it says 8–10). Drain, rinse with cold water, and transfer to an ice bath to stop cooking. Set aside and let cool completely.
In a blender, food processor, or using an immersion blender, blend ¾ cup cottage cheese until completely smooth. You should end up with roughly ⅓ cup of whipped cottage cheese.
In a large mixing bowl, whisk together the whipped cottage cheese, mayo, vinegar (start with 3 tablespoons), salt, sugar, and a splash of pickle juice. Taste and adjust vinegar or salt if needed—the flavor should be tangy and well-seasoned.
While the pasta cools, finely dice the pickles, celery, bell pepper, and red onion. If the onion tastes too strong, soak it in ice water for 5 minutes, then drain. Add the cooled pasta and all the diced veggies to the bowl with the dressing. Stir gently until everything is evenly coated.
Refrigerate for at least 30 minutes before serving to let the flavors meld. Make-ahead tip: If preparing in advance, reserve half the dressing and stir it in just before serving to prevent the pasta from drying out.