Place the potatoes in a large pot and cover with cold water by about 1-inch. Bring to a boil, then reduce the heat and simmer, uncovered, until fork-tender, about 10 minutes. Drain the potatoes, set aside to cool to room temperature, then transfer to a large bowl.
Make the dressing: In a medium bowl, whisk together the yogurt, mayo, mustard, lemon juice, olive oil, garlic, salt, turmeric, if using, and several grinds of pepper. Note: this will taste strong and salty at this step; it’ll balance once it’s mixed with the potatoes.
Pour the dressing over the potatoes and stir to coat. Stir in the celery, red onions, capers, radishes, chives, and dill and celery seed, if using. Season to taste and garnish with the reserved radishes and chives.