Is he required to perform the prostration of forgetfulness (sujood as-sahw) for repeating the latter part of the final tashahhud in prayer, due to the worshiper’s doubt as to whether he had recited it or not, and then he did not perform the prostration of forgetfulness?

Sending blessings upon the Prophet (peace be upon him) in the final tashahhud is a point of scholarly disagreement. The view of the Shafi'is and Hanbalis, that it is a pillar, is more cautious. What suffices for it is saying: "اللهم صل على محمد" (O Allah, send blessings upon Muhammad).

Whoever doubts whether they performed a pillar must perform it. And whoever doubts whether they omitted a recommended saying while it was due, it is legislated for them to perform it. As for someone who repeated an obligatory utterance in prayer, prostration of forgetfulness (sujud al-sahw) is legislated for them, but prostration is not legislated for repeating something that is not obligatory. Therefore, what the person mentioned, that sujud al-sahw for repeating the phrase: "وبارك على محمد" (and bless Muhammad) due to doubt is not required, is correct.