Is what the worshiper did—returning to the position of the final tashahhud immediately after the taslim to correct an error in the final tashahhud, pronouncing the takbir while seated without raising the hands, then completing the tashahhud and the taslim, and performing the sujud al-sahw—religiously sound, or should he have returned to the sujud before the tashahhud, and would he then pronounce the takbir?

If a worshiper doubts, after the prayer, an error in the wording of the tashahhud, then their prayer is valid, and they are not required to repeat it, because the original state is its validity. They were not correct in repeating the tashahhud, and their prayer is not invalidated by that. For one who is required to repeat the tashahhud, it is not prescribed for them to prostrate before it to say their tashahhud after rising from prostration, nor are they required to repeat the takbir for rising from prostration after the takbir.