Lower bound $\Omega$ grows quicker than upper bound $O$ of a recurrence relation $T(n)$?
You calculated “Big-Theta for n = power of two - 1”. That’s not a useful thing. Try calculating T(n) for n = (4^k - 1) / 3 and be surprised. (Write n down in binary first). Or n = 3 * (8^k - 1) / 7 where T(n) ≈ n^(2/3).
You found the values for a good case and for a bad case. You’ll have to prove they are lower and upper bound.