Is it sunnah to say "wa barakatuhu" while saluting at the end of the prayer? Will you evaluate the narrations regarding the issue?
One source of this is:
I offered prayer along with the Prophet (ﷺ). He would give the salutation to his right side (saying): Peace be upon you and the mercy of Allah and His blessings; and to his left side (saying): Peace be upon you and mercy of Allah. (Sunan abi Dawod)
so the addition "wa barakatuhu" (and His blessings) is only confirmed for the right side tasleem!
Al-Aabadi his 'Awn al-Ma'abod عون المعبود -see here in Arabic-when discussing this hadith quoted that ibn Hajar commented on an-Nawawi's al-Adkhar in his book Talqeeh al-Afkaar fi Takhrij al-Adhkaar تلقيح الأفكار تخريج الأذكار by quoting different ways (hadith chains) that quote this addition the hadith quoted above appears without this addition on the authenticity of at least 15 of the sahabah as ibn Hajar said, and he added that the addition of a trustworthy narrator must be accepted. And Wa'il is such a narrator!
Ibn Bazz in this fatwa in Arabic didn't approve this addition, but said if one believes it is sunnah then the prayer would be accepted. Else he said it is better not to add this as this is a discussed matter and the hadith is said to have some flaws.