Preheat the oven to 375°F (190°C).
Using a sharp knife, carefully cut a pocket into each chicken breast by slicing horizontally through the thickest part, being careful not to cut all the way through.
In a medium bowl, combine the chopped spinach, crumbled feta cheese, chopped red onion, minced garlic, dried oregano, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Mix well.
Stuff each chicken breast pocket evenly with the spinach and feta mixture.
Heat olive oil in an oven-safe skillet over medium-high heat. Once hot, add the stuffed chicken breasts and sear for 3-4 minutes on each side until golden brown.
Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).
While the chicken is baking, prepare the Greek yogurt sauce. In a small bowl, combine the Greek yogurt, fresh lemon juice, chopped dill, garlic powder, and a pinch of salt and black pepper. Stir until smooth.
Remove the chicken from the oven and let it rest for 5 minutes.
Serve the stuffed chicken breasts hot with a generous spoonful of the Greek yogurt sauce on top or on the side.