Cut each chicken breast into three long, wide strips. Mix all the marinade ingredients, then add to the chicken. Let marinate for at least 2 hours.
Meanwhile, prepare the yogurt and cucumber sauce. Put the grated cucumber in a strainer, add the salt, stir and let rest for 20 minutes. Then squeeze to eliminate as much liquid as possible. Mix the cucumber with the yogurt, dill, garlic, juice, and zest. Mix until all the ingredients are well integrated. Season with salt (if needed) and pepper. Set aside and refrigerate until ready to serve.
Place the stainless steel inner pot inside the Instant Pot®. Press Saute and set time to 8 Minutes. Add the oil. Once hot, add the breast strips, lightly browned on both sides. Take out of the pot and set aside. When done, press Cancel.
Without rinsing the Instant Pot® bowl, now put in the chicken broth, the rack, and on top of that the chicken breast strips covered with the marinade.
Close and lock the Instant Pot® lid. Make sure the steam release handle is turned to Sealing. Press Pressure Cook, pressure level High, and set time to 8 Minutes.
When done, press Cancel and turn the steam release handle to Venting. Once all the pressure is released, open the lid and remove the chicken.
To serve, put a little yogurt and cucumber sauce on each pita, a couple of chicken strips, tomato salad, and feta cheese. Serve immediately with black olives on the side.