It does not say in Hebrews 8:6-10 that the fault that God found with the Mosaic Covenant was with His law, but with the people for not continuing to obey it, which is why the New Covenant involves God putting His law in our minds and writing it on our heart so that we will obey it. In Psalms 119:29-30, he wanted to put false ways far from him, for God to be gracious to him by teaching him to obey the Mosaic Law, and he chose the way of faith by setting it before him, so this has always been the one and only way of salvation by grace through faith. In Exodus 33:13, Moses wanted God to be gracious to him by teaching him to walk in His way that he and Israel might know Him, in 1 Kings 2:1-3, God taught how to walk in His way through the Mosaic Law, and in John 17:3, eternal life is knowing God and Jesus, which is again salvation by grace through faith. The Mosaic Law is God's instructions for how to believe in Him, so we can't believe in Him instead of obeying His instructions for how to do that. Those under the New Covenant don't need to be taught to know God because it involves God's instructions for how to know Him being put in our minds and written on our hearts, so the problem is that many
people want nothing to do with the New Covenant.
Philippians 3:1Finally, my brethren, rejoice in the Lord. To write the same things to you, to me indeed is not grievous, but for you it is safe. 2 Beware of dogs, beware of evil workers, beware of the concision. 3 For we are the circumcision, which worship God in the spirit, and rejoice in Christ Jesus, and have no confidence in the flesh. 4 Though I might also have confidence in the flesh. If any other man thinketh that he hath whereof he might trust in the flesh, I more: 5 Circumcised the eighth day, of the stock of Israel, of the tribe of Benjamin, an Hebrew of the Hebrews; as touching the law, a Pharisee; 6 Concerning zeal, persecuting the church; touching the righteousness which is in the law, blameless.
7 But what things were gain to me, those I counted loss for Christ.
8 Yea doubtless, and I count all things but loss for the excellency of the knowledge of Christ Jesus my Lord: for whom I have suffered the loss of all things, and do count them but dung, that I may win Christ,
9 And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith:
The Mosaic Law is God's word and Jesus is God's word made flesh, so it is contradictory to believe in Jesus instead of obeying the Mosaic Law. The Son is the radiance of God's glory and the exact image of His nature (Hebrews 1:3), so Jesus embodied God's nature by setting a sinless example of walking in obedience to the Mosaic Law and the way to believe in him is by following his example. For instance, by doing good works in obedience to the Mosaic Law we are testifying about God's goodness, which is why our good works bring glory to Him (Matthew 5:16), and by testifying about God's goodness, we are also expressing the belief that God is good, or in other words, we are believing in Him. Likewise, doing what is holy, righteous, just, merciful, faithful, and so forth in accordance with Christ's example is the way to believe that he is those traits, or in other words, it is the way to believe in him. This is why there are many verses that connect our faith in God with our obedience to His commands, such as Revelation 14:12, where those who kept faith in Jesus are the same as those who kept God's commands.
Our salvation is from sin (Matthew 1:21) and it is by the Mosaic Law that we have knowledge of what sin is (Romans 3:20), so while we do not earn our salvation as a wage as the result of having first obeyed it, living in obedience to it through faith in Jesus is nevertheless intrinsically part of the gift of him saving us from not living in obedience to it.
Do you differentiate from looking to yourself in keeping the law of Moses to Christ in helping you to abide in His words which is higher than the works of the law?
Either Paul only spoke against becoming circumcised for incorrect purposes or according to Galatians 5:2, Paul caused Christ to be of no value to Timothy when he had him circumcised right after the Jerusalem Council (Acts 16:3) and Christ is of no value to roughly 80% of them men in the US.
I would say from your point of view that this rebuke by Paul seems unfounded if it mean getting them to keep the laws of Moses entirely.
Galatians 5:1
Stand fast therefore in the liberty wherewith Christ hath made us free, and be not entangled again with the yoke of bondage. 2 Behold, I Paul say unto you, that if ye be circumcised, Christ shall profit you nothing. 3 For I testify again to every man that is circumcised,
that he is a debtor to do the whole law. 4 Christ is become of no effect unto you, whosoever of you are justified by the law; ye are fallen from grace.
5 For we through the Spirit wait for the hope of righteousness by faith.
And how is this righteousness by faith comes about in the life of a saved believer? Not by our religious flesh.
Galatians 3:1O foolish Galatians, who hath bewitched you, that ye should not obey the truth, before whose eyes Jesus Christ hath been evidently set forth, crucified among you? 2 This only would I learn of you, Received ye the Spirit by the works of the law, or by the hearing of faith? 3 Are ye so foolish? having begun in the Spirit, are ye now made perfect by the flesh? 4 Have ye suffered so many things in vain? if it be yet in vain. 5 He therefore that ministereth to you the Spirit, and worketh miracles among you, doeth he it by the works of the law, or by the hearing of faith? 6 Even as Abraham believed God, and it was accounted to him for righteousness. 7 Know ye therefore that they which are of faith, the same are the children of Abraham.
8 And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed. 9 So then they which be of faith are blessed with faithful Abraham.
10 For as many as are of the works of the law are under the curse: for it is written, Cursed is every one that continueth not in all things which are written in the book of the law to do them. 11 But that no man is justified by the law in the sight of God, it is evident: for,
The just shall live by faith. 12 And the law is not of faith: but, The man that doeth them shall live in them. 13 Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is every one that hangeth on a tree:
14 That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith.
21 Is the law then against the promises of God? God forbid: for if there had been a law given which could have given life, verily righteousness should have been by the law. 22 But the scripture hath concluded all under sin, that the promise by faith of Jesus Christ might be given to them that believe. 23 But before faith came, we were kept under the law, shut up unto the faith which should afterwards be revealed. 24
Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith. 25 But after that faith is come, we are no longer under a schoolmaster. 26 For ye are all the children of God by faith in Christ Jesus. 27 For as many of you as have been baptized into Christ have put on Christ. 28 There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus. 29 And if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise.
The Jerusalem Council did not rule that Gentiles were not under the Mosaic Law. In Acts 15:11, it makes it clear that Acts 15:10 was not referring to the Mosaic Law as being a heavy burden that no one could bear, but rather the heavy burden was an alternative to salvation by grace, namely salvation by circumcision that was proposed in Acts 15:1. The purpose for which God commanded circumcision was not in order to become saved, so the Jerusalem Council upheld the Mosaic Law by correctly ruling against requiring circumcision for an incorrect purpose. The Jerusalem Council did not have the authority to countermand God, so they should not be interpreted as ruling against Gentiles obeying the Mosaic Law, which would be ruling that Gentles shouldn't believe in Christ or have the gift of salvation.
Since the matter was about the need for Gentiles to be circumcised
and to keep the law of Moses, one would think per your answer, that they would have defer from circumcision but to be clear that the Gentiles had to keep the laws of Moses, but no. They only addressed those sins that the Gentiles were exposed to. They certainly were not taught to keep the sabbath which the Gentiles believers were not doing before they were saved.