I read my friend’s notes about Diodorus’ (fourth century C.E.) description of the Antiochene school of biblical interpretation, which is literal. One key term for the Antiochenes is “prosopon”, which (in my friend’s words) “is the point of view of the speaker (David speaking from the prosopon of Hezekiah).”
I think this means that there are times when David speaks from the perspective of a future figure, such as Hezekiah and Jesus, as if David is a prophet. Acts 2:25-30 presents David speaking as a prophet, foretelling the resurrection of Christ. Yet, David speaks in the first person, as if he is taking the perspective of Jesus.