Whisk the yogurt, 2 tbsp olive oil, 2 tbsp lemon juice, 4 minced garlic cloves, oregano, cumin, paprika, 1 1/2 tsp salt and pepper in a mixing bowl. Add the thighs and turn to coat. Cover and refrigerate for 30 minutes, or up to 8 hours.
Make the tzatziki while the chicken marinates. Squeeze the grated cucumber in a clean kitchen towel until it stops dripping, then stir it into the 240 g yogurt with the grated garlic, 1 tbsp lemon juice, 1 tbsp olive oil, dill and 1/4 tsp salt. Cover and refrigerate.
Heat the oven to 220 C / 425 F with a rack in the middle. Line a 33 x 46 cm / 13 x 18 inch rimmed sheet pan with parchment. Toss the peppers and red onion on the pan with 1 tbsp olive oil and 1/2 tsp salt.
Wipe the excess marinade off each thigh with the back of a spoon. Set the thighs on the pan between the vegetables in a single layer with gaps. If the vegetables overlap they steam and turn soft instead of browning, so move half to a second pan if needed.
Roast for 15 minutes, then scatter the cherry tomatoes over the vegetables. Roast 10 minutes more, for 25 minutes total, until the edges of the chicken are browned and the thickest thigh reads 175 F / 79 C.
Move the chicken to a cutting board and rest it for 5 minutes. Turn the oven off, wrap the pitas in foil and warm them in the hot oven during the rest. Slice the chicken against the grain into strips about 5 mm thick.
Fill each pita with sliced chicken, roasted vegetables, tzatziki, crumbled feta and olives. Serve right away while the pita is warm.