Isaiah 2:1-4 depicts the exaltation of Jerusalem, the salvation that comes through and after the judgment of exile. Isaiah 2:4 reads in part:
they shall beat their swords into plowshares, and their spears into pruning hooks; nation shall not lift up sword against nation, neither shall they learn war anymore. (Isa 2:4 ESV)
Isaiah 9:1-7 is talking about that same salvation that comes through judgment (for God’s glory), and Isaiah 9:5 gives another take on the peace described in Isaiah 2:4
For every boot of the tramping warrior in battle tumult and every garment rolled in blood will be burned as fuel for the fire. (Isa 9:5 ESV)
So while Isaiah 2 may not explicitly mention the Messiah reigning at the glorious eschatological restoration, he’s in view in Isaiah 9:6, and Isaiah 9:5 is talking about the same thing as Isaiah 2:4. So who do you think is going to “judge between the nations, and . . . decide disputes for many peoples” (Isa 2:4)?