Place tofu onto a plate lined with several paper towels. Cover tofu with more paper towels and another plate. Set a 3- to 5-pound weight on top and press tofu for 30 minutes. Drain and discard any accumulated liquid and cut tofu into 1/2-inch cubes.
Place cubed tofu into a large bowl and drizzle with sesame oil. Gently stir and let sit for 20 minutes.
Meanwhile, make bang bang sauce by whisking together mayonnaise, sweet chili sauce, and Sriracha sauce in a medium bowl until smooth. Place bread crumbs in a separate bowl.
Preheat the air fryer to 400 degrees F (200 degrees C).
Mix tofu with 1/2 cup bang bang sauce until evenly combined. Coat tofu in bread crumbs and place in the air fryer basket, making sure tofu pieces do not overlap. Depending on the size of your air fryer, you may need to do this in batches.
Cook in the preheated air fryer for 5 minutes. Shake and cook for 3 minutes more. Garnish with green onion and serve with remaining bang bang sauce.