Preheat the oven to 350°F (180°C).
Place the chicken thighs skin side up in a roasting pan or large rimmed baking sheet. Drizzle over the oil and sprinkle over the smoked paprika, oregano, and 1 teaspoon each of salt and pepper.
Add the onion, cherry tomatoes, and semi-dried tomatoes to the pan, cover with foil and roast until the chicken is browned and the tomatoes are beginning to burst, about 1 hour.
Remove the foil and stir in the sugar, Worcestershire sauce, vinegar, tomato paste, and chicken stock. Place the pan back in the oven and cook until the chicken is tender and cooked through to an internal temperature of at least 165°F (74°C), about 30 minutes more.
Towards the end of the chicken cooking time, cook the bucatini in a large pot of boiling, salted water, according to the package instructions.
Remove the pan from the oven and use 2 forks to carefully shred the meat, discarding the bones and skin. Stir and mash everything together to make a chunky sauce.
Drain the pasta in a colander, reserving a cupful of cooking water. Tip the pasta into the roasting pan, with a good splash of pasta water. Toss everything together and serve.