Preheat oven to 400 degrees F. Spread sweet potato tots in a single layer across two parchment-lined baking sheets, leaving space between each piece. Bake for 10 minutes to soften.
Meanwhile, add mayonnaise, Greek yogurt, Dijon mustard, lemon juice, salt, black pepper, and smoked paprika to a large bowl. Whisk to combine. Fold in fresh dill, green onions, chopped pickles, and celery. Cover and refrigerate until ready to use.
Remove sweet potato tots from oven. Using the flat bottom of a drinking glass, press firmly on each tot to smash into a flat disc. Season generously with kosher salt.
Return to the oven and bake for an additional 25 minutes, about 10 minutes longer than package directions, until the edges are deep golden. Sweet potato tots won't crisp the same way regular tater tots do, so you're looking for set, golden edges rather than crunch.
Let the tots cool for about 5 minutes, then fold them into the dressing with half of the feta cheese, and stir gently to coat. The tots will absorb the dressing as they sit, making for a cohesive, flavorful bite throughout.
Transfer to a serving dish, top with remaining crumbled feta and extra fresh dill, as desired. Serve immediately.