Is God finished with Israel? Is He done with the Jewish people as a people?
Different questions.
Who is "Israel", according to biblical usage?
RE: Who is “Israel”, according to biblical usage?
It is literally used to refer to the Nation of Israel ( those who are PHYSICALLY DESCENDED from Abraham).
However, it is also spiritually used to refer to the Church as the “Israel of God” ( Which includes those who are physical descendants of Abraham as well as those who are spiritual descendants of Abraham by faith. See for instance Galatians 6:15-16).