The OT historical-background regarding the Servant of the Lord was not understood as messianic in function, but was mysterious or symbolic because the intertestamental-period Judaism's interpretation of the Messiah was militaristic not a servant, and in postbiblical-period Judaism there is no evidence identifying these songs as messianic since Christians claimed it.
Hence, first century Christians understood these texts as messianic because they found strong evidence in the life and fulfillment of Jesus Christ as servant [i.e. typology]. Below are the four classic texts regarded as the "Servant Songs" of Isaiah. As Schreiner points out that these passages "are represented by a particular person, one who atones for the sin of the people [i.e. Jesus Christ]."
There are four poetic passages known in the OT as the "Songs of the Servant of Yahweh":
1. First Song: The servant proclaims he is the chosen one and given the Spirit to establish justice (42:1–4).
2. Second Song: The servant reveals and identifies himself as one called by God before birth for the nations (Isa. 49:1-6).
3. Third Song: The servant declares his confidence in God even in the face of oppression and persecution (Isa. 50:4-11).
4. Fourth Song: The servant suffers and dies on behalf of others so they can be healed (Isa. 52:13-53:12).
As a result, the Servant Songs in Isaiah identify the Servant of the Lord as a king, prophet, and new Moses. Israel is identified as the children of Abraham, his chose servant (cf. Isa. 41:8-9; 44:1-2; 45:4). God's chosen servant, Israel, fails to see and hear God's word making them flawed and sinful. Thus, the Servant of the Lord suffers and dies for them to forgiven and redeem them from exile (cf. Isa. 44:21-22; 48:20).
These theological realities were not realized until the coming of one like the Son of Man, Jesus Christ. The Servant of the Lord is personified in the person of Jesus Christ, who as servant is both Israel and transcends Israel because he is chosen by God the Father, and fulfills the requirements and commandments given to Israel. Therefore, it is appropriate to say that the "gospel according to Isaiah 53" is displayed by the righteous Servant of the Lord who suffered and died for the sake of transgressors. Amen!