Place the peeled potatoes in a large pot and cover with salted water. Bring to a boil over medium-high heat, then reduce to a simmer and cook until they are just tender when pierced with a fork, about 15-20 minutes.
Drain the potatoes thoroughly in a colander and let them cool slightly for a few minutes. Peel and chop the potatoes into bite-sized pieces while still warm, which helps them mash easily.
In a large mixing bowl, gently mash the warm potatoes with a fork or potato masher until smooth and fluffy, feeling the soft resistance give way as they break apart.
Add the mayonnaise, vinegar, and mustard to the mashed potatoes. Mix well until the mixture is creamy and smooth, ensuring all the potatoes are coated evenly.
Fold in the chopped celery and soaked red onion, giving the salad a satisfying crunch and sharpness with each bite.
Stir in the freshly chopped herbs and season with salt and pepper to taste. Adjust the seasoning as needed, tasting for brightness and balance.
Cover the bowl with plastic wrap and refrigerate for at least an hour to let the flavors meld and the salad chill thoroughly.
Once chilled, give the salad a gentle stir to redistribute the flavors, then serve it cold, garnished with extra herbs if desired.