Position oven racks in top third and lower third; preheat to 425°F. Line 2 large rimmed baking sheets with parchment paper. Cut squash into 1/2-inch-thick strips (about 4 to 5 inches long).

Place the squash strips in a colander placed over a large bowl; pat dry using paper towels, if needed, to remove excess moisture. Sprinkle evenly with cornstarch; toss to coat, shaking the colander to remove excess cornstarch. Discard excess cornstarch.

Combine panko, onion powder and paprika in a shallow medium bowl until combined. Place eggs in a separate shallow medium bowl.

Working with 1 squash piece at a time, dip in egg mixture, letting excess drip off. Dredge in panko mixture. Arrange in a single layer on the prepared baking sheets, at least 1/2-inch apart. Coat the fries generously with cooking spray.

Bake until golden and crispy, 20 to 25 minutes, rotating baking sheets between top and bottom racks and from front to back halfway through.

Meanwhile, place 1/4 cup yogurt, feta, lemon juice, and 1/4 teaspoon salt in a food processor; pulse until combined, about 5 pulses (the mixture will be slightly lumpy). Add the remaining 3/4 cup yogurt. With the processor running, gradually pour oil through the chute, processing until very smooth, about 2 minutes, stopping to scrape down the sides of the bowl as needed. Transfer to a shallow bowl; top with parsley and pepper.

Sprinkle the fries with the remaining 1/4 teaspoon salt. Serve with feta sauce.