Is it obligatory to perform the prostration of forgetfulness (sujud al-sahw) and repeat the prayer if one did not complete the salutation upon the Prophet in the final tashahhud, and then completed it before the taslim?

Praying for the Prophet after the Tashahhud is one of the Sunan (recommended acts) of prayer according to most scholars, and it is compensated for by the prostration of forgetfulness (Sujud as-Sahw). Prayer is not invalidated by omitting it. Even according to those who consider it a pillar (rukn) or an obligation (wajib), the prostration of forgetfulness is not required, nor is the prayer invalidated, if the worshipper performs the sufficient part of it, which is "Allahumma Salli ala Muhammad" (O Allah, send blessings upon Muhammad). And if one prays for the Prophet before the salutation (taslim), their prayer is valid and they are not required to perform the prostration of forgetfulness.