What are the sources that mention that Mu'awiyah ibn Abi Sufyan, may Allah be pleased with him, was one of the scribes of revelation, and is everything mentioned in those sources trustworthy?

Mu'awiyah (may Allah be pleased with him) was a scribe for the Messenger of Allah (peace be upon him). Evidence for this is what Imam Ahmad narrated in Al-Musnad with a sound chain of transmission from Ibn Abbas (may Allah be pleased with both of them), who said that he was a young boy when the Prophet (peace be upon him) called him and said: "Go and call Mu'awiyah for me." So Ibn Abbas went and called Mu'awiyah, who was the scribe of the Prophet (peace be upon him).