Slice the chicken breasts into roughly 1-inch-wide strips.
In a large bowl or ZipLoc bag, combine the olive oil, garlic powder, Worcestershire sauce, ground cumin, dried oregano, lemon juice from 1/2 lemon, and salt and pepper; add the chicken strips and the rosemary sprigs, then refrigerate to marinate for at least 30 minutes and up to 2 hours.
Prepare the yogurt sauce by peeling and grating the zucchini into a bowl, then stir in the Greek yogurt, minced garlic, torn basil leaves, and salt and pepper to taste; refrigerate until ready to serve.
If using wooden skewers, soak them in water for at least 10 minutes. Thread the marinated chicken strips onto skewers, removing the rosemary sprigs from the marinade to place on top of or alongside the chicken when grilling.
If making orzo, bring a pot of salted water to a boil and cook the orzo according to package directions; drain and toss with about 1/2 teaspoon olive oil to prevent sticking, then transfer to a bowl and keep warm.
Preheat the grill to high, then reduce to medium-high before cooking. Place the skewers on the grill and cook 4–5 minutes per side, until cooked through and the juices run clear.
Grill the halved lemon cut-side down for about 7 minutes until charred; grill the rosemary sprigs on top of the meat with the lid closed, or place them directly on the grill for a few minutes if using an uncovered grill, until crispy.
Serve the chicken skewers with the yogurt sauce, orzo or naan, crispy rosemary sprigs, and charred lemon.