Moses gave the law but only to the Jews - no one else.
Jesus gave us the new covenant, replacing the old covenant, not doing away with the Law but fulfilling/perfecting it. Christians are under Grace [unmerited/undeserved favor] and our law is to love God with all our heart and love others as ourselves [and walk in the Spirit].
Paul wrote extensively about those Jews who attempting to bring the church back under the law but he said if you go back to the law you make Christ of none effect.
I’ve cut and pasted your post for future reference because you put it so well in just a few lines. Thanks!