What is the ruling on the prayer of one who, by mistake, said the Tasleem in the second raka’ah, thinking it was the last, then completed the raka’at and performed the prostration of forgetfulness, then repeated the prayer due to a confusion of intention? Is his action correct?

What you did, by completing the prayer and performing the prostration of forgetfulness (sujud al-sahw) after the salam, is correct. Your prayer is therefore valid, and you are not required to repeat it, provided that you had intended to pray Asr at the beginning of the prayer. For it is not obligatory to maintain the awareness of the intention throughout the prayer, and the mind's distraction from the intention during worship does not invalidate it. Likewise, it does not matter if you thought you were praying a different prayer than the one you intended, as long as you formed the intention at its legally recognized time.