I should slightly qualify my last comment. I used “supra Jewish identity” in the sense of an overarching Jewish identity which would have come from any restored Israel. This is different from the way you were using it. My argument is that there is no restored Israel, no “Jewish empire”, no “supra Jewish identity”.
Also, the law prevented Gentiles from “getting in” to the privileges which came with being part of the Jewish nation and God’s people (covenant, law, temple). This is summed up with the word “access”. Because of the law, Gentiles did not have access to, or were kept at a distance from, the closer proximity to God enjoyed by Jews through their status in the covenant, or in the temple, for instance. Paul uses the word to describe how Jesus removed the “dividing wall” by providing in himself “access” to grace, to the father by one spirit, to God. To “enter” (the presence and privileges of God), gentiles needed only faith in Jesus (Romans 5:2, Ephesians 2:18, Ephesians 3:12). Membership of a restored Israel was neither a precondition nor a consequence of this access, and is not mentioned as such.