Place the frozen blueberries in a microwave-safe bowl and microwave until defrosted, 1 to 2 minutes. Allow to cool to room temperature, 3 to 5 minutes; do not drain.

Whisk flour, baking powder, and salt together in a small bowl until well combined.

Transfer cooled blueberries and juice to a large bowl. Add sugar and oil and whisk until thoroughly combined. Mix in egg whites, lemon zest, and vanilla until thoroughly incorporated. Add flour mixture in 2 batches, mixing after each addition until just combined. Cover and refrigerate for at least 2 hours.

Preheat the oven to 400 degrees F (200 degrees C). Line 2 baking sheets with parchment paper.

Prepare coating ingredients by placing each sugar in a separate small bowl.

Remove dough from the refrigerator. Scoop 1 1/2 tablespoons dough and carefully shape into a ball (the dough will still be kind of soft and sticky.) Coat the ball in white sugar, then drop into powdered sugar and roll to thoroughly coat. Place on a prepared baking sheet. Repeat the process with the remaining dough, spacing cookies 1 1/2 inches apart on the baking sheets.

Bake in the preheated oven until cookies are just set, 8 to 10 minutes, switching racks halfway through. Cool on the baking sheet briefly before removing to a wire rack to cool completely.