Set the Ninja Foodi to Sear/Sauté on High. Add the olive oil and ground beef. Season with the Greek seasoning, garlic powder, and salt. Cook, breaking apart, until completely browned and cooked through.
Transfer the cooked beef to a bowl and set aside. Leave the drippings in the pot.
Add the diced yellow squash, zucchini, and red onion directly to the beef drippings. Season with 2 teaspoons of Greek seasoning and a small drizzle of olive oil if needed. Sauté just until slightly tender — you want them to still have a little bite. Don't overcook.
Return the ground beef to the pot and stir to combine. Turn off the Ninja Foodi and cover to keep warm.
While the filling stays warm combine the diced cucumbers, cherry tomatoes, and Kalamata olives in a small bowl. Stir and set aside.
Warm the pita bread in a dry skillet or quickly over a gas burner until soft, warm, and flexible.
Spread a generous layer of hummus over each warm pita. Add the beef and vegetable mixture then spoon the cucumber, tomato, and olive topping over. Drizzle generously with tzatziki, fold, and serve immediately.