Make the marinade: In a bowl, whisk all marinade ingredients except the bay leaves. Taste a tiny drop; it should be bright and savory.
Marinate the chicken: Reserve 2 Tbsp marinade in a clean cup for basting. Toss chicken with the remaining marinade and the crumpled bay leaves. Cover and refrigerate 30 minutes–12 hours.
Make tzatziki: Stir yogurt, squeezed cucumber, olive oil, lemon juice, garlic, dill/mint, and the optional pinch of salt with pepper. Chill 15 minutes.
Preheat: Oil grill or ridged grill pan and heat to medium-high (about 450–500°F). For a grill pan, heat until a few wisps of smoke appear.
Skewer: Remove and discard bay leaves. Thread chicken onto 8 skewers with slight gaps; discard used marinade.
Grill: Cook 8–10 minutes total, turning every 2–3 minutes. Brush once with the reserved clean marinade during the final minutes. Cook to 165°F in the center; rest 3 minutes.
Warm pitas: Heat 15–30 seconds per side until pliable and lightly charred.
Assemble: Spread tzatziki in each pita, add chicken, tomato, cucumber, a few onion slivers, and 2 olive halves. Finish with herbs and serve with lemon wedges.