To prepare the chicken, mix the Greek yogurt, garlic, smoked paprika, oregano, and salt in a bowl. Thoroughly coat the chicken breasts in the mixture, then cover and let them marinate for 30 minutes or longer.
Transfer the chicken to your air fryer. Air fry at 360°F (180°C) for approximately 18 minutes, making sure to flip the pieces over at the nine-minute mark so they cook evenly and turn golden brown.
While the chicken cooks, assemble the salad base by mixing the cucumber, tomatoes, bell pepper, red onion, and olives in a large container.
Prepare the vinaigrette by whisking lemon juice, olive oil, oregano, salt, and pepper in a small dish.
Drizzle the vinaigrette over the salad and toss well.
Allow the cooked chicken to rest for 5 minutes before slicing it.
Place the chicken slices over the salad, garnish with crumbled feta, and serve immediately.