"Say" and "said" as transitive and intransitive verbs

I have an interesting question. Is “say” a transitive verb in the case of direct/reported speech? I understand that it can be a transitive verb in cases like “She said the phrase.” or “She says the words quietly.”. But what about:

Bob looked at his fried and said, “You are my best buddy.”
Or, “I know that,” said his friend.

My thought process on this is that the direct/reported speech instance is not representing the use of the verb “say” as transitive, as it is a separate dialogue tag with no direct object. However, I think this all moves into the realm of what we believe the role of speech is in grammatical structure in the first place, which I don’t know about you, but I have mixed thoughts on in the first place.