“he will reign over the house of Jacob forever,” This verse is a good example that just because something in scripture is said to last forever, doesn’t mean it starts immediately. Likewise, even though we have eternal life (John 3:15-16, 36), it does not mean it comes into effect immediately; because if the Lord tarries we will still die and need to be resurrected into that eternal life: “Everyone who looks to the Son and believes in him shall have eternal life, and I will raise him up at the last day” (John 6:40, NIV).
Saying, “the house of Jacob” points back to Jacob and all 12 of his sons, so the Messiah was not just a king over the Judeans, but over all Israel, and then by extension over the whole world.