Is what the worshiper did—interrupting the Tashahhud and standing up to complete the fourth rak‘ah, then performing the prostrations of forgetfulness (sujud al-sahw) after the salām—correct, given that he doubted the number of rak‘ahs (three or four) during the final Tashahhud in the ‘Ishā’ prayer?

What you did is correct, because the duty of one who doubts in their prayer is to cast aside the doubt and build upon what they are certain of. It is preferable to perform the prostration of forgetfulness (sujud al-sahw) before the salutation (taslim), but your prostration after it does no harm, because prostrating before or after the salutation is permissible. The difference is only in what is more virtuous. This is supported by the saying of the Messenger of Allah, peace and blessings be upon him: "If one of you doubts in his prayer and does not know whether he prayed three or four (rak'ahs), he should cast aside the doubt and build upon what he is certain of. Then he should perform two prostrations before he gives the salutation. If he had prayed five (rak'ahs), these two prostrations would make his prayer an even number for him, and if he had prayed a complete four (rak'ahs), they would be a humiliation for the Devil."