Grate the zucchini and place it in a clean kitchen towel or several layers of paper towels; squeeze firmly to remove all moisture until about 4.25 oz of drained zucchini remain.
In a large bowl, combine the drained zucchini, ground turkey, breadcrumbs, grated garlic, grated red onion, kosher salt, and fresh ground pepper.
Mix gently until just combined, then divide the mixture into 5 equal portions and form each into a patty about 4 ounces and 1/2 inch thick.
Stovetop: Heat a large nonstick skillet over high heat, lightly spray with oil, add the patties, reduce heat to low, and cook until browned on one side; flip and continue turning occasionally until cooked through and no longer pink in the center.
Grill: Clean and oil the grill; cook patties over medium heat about 5 minutes per side or until no longer pink in the center.
Air fryer: Preheat to 370°F (188°C). Arrange patties in a single layer (cook in two batches if needed) and cook 10 minutes, turning halfway, until browned and cooked through.
Serve the burgers hot on buns or as desired.