Grate about half of a medium yellow onion using the fine side of a box grater. Measure out 2 tablespoons of the grated onion, leaving behind as much of the liquid as possible. Measure and prepare all seasonings.
In a large bowl, combine the ground turkey, grated onion, Worcestershire sauce, olive oil, garlic powder, smoked paprika, salt, and pepper. Mix with clean hands until just incorporated. Do not overmix.
Divide the mixture into 4 equal portions (about 4 oz each). Lightly wet your hands, then shape each portion into a patty about ½ inch thick and 4 inches wide. Use your thumb to create a shallow indent in the center of each patty. Refrigerate for 20-30 minutes if time allows.
Preheat the air fryer to 375°F (190°C) for 5 minutes. Spray the air fryer basket lightly with cooking spray or place a pre-cut parchment liner in the bottom.
Place the turkey patties in the air fryer basket in a single layer, leaving at least ½ inch of space between each. Air fry at 375°F for 6 minutes, then carefully flip each patty. Continue air frying for another 5-6 minutes.
Insert an instant-read meat thermometer into the thickest part of a patty. Cook until the internal temperature reaches 165°F (74°C). Remove from the air fryer and let rest for 2 minutes.
Optional: For a cheeseburger, place a slice of cheese on each patty, close the air fryer (turned off) for about 60 seconds to melt. Toast buns cut-side down in the air fryer at 375°F for 1-2 minutes.
Assemble the burgers by spreading your preferred condiment on the bottom bun, layering with lettuce, the turkey patty, tomato, and red onion. Top with the other bun half and serve immediately.