What did “Messiah” mean before Yeshua was born?

Part of a series: questions that make more sense when the Tanakh and the New Testament are read together.

Psalm 2 already has a coronation formula — God's anointed king, installed on Zion, the nations given to him as an inheritance — centuries before Yeshua. Luke's angel echoes it almost word for word: “the Lord God will give him the throne of his father David… and of his kingdom there will be no end” (Luke 1:32–33).

So: was Yeshua's messiahship a new category, or the fulfillment of an office Israel's own scriptures had already defined? Bring your sources.