The only covenant that God remembers our sins no more is with Israel
Heb 8:10 For this is the covenant that I will make with the house of Israel after those days, says the Lord: I will put My laws in their mind and write them on their hearts; and I will be their God, and they shall be My people. 11None of them shall teach his neighbor, and none his brother, saying, ‘Know the Lord,’ for all shall know Me, from the least of them to the greatest of them. 12;For I will be merciful to their unrighteousness, and their sins and their lawless deeds I will remember no more.”
We enter this covenant not by nationality but by faith and receive all of the promises that came through the bloodline of Abraham, including the Blessing God gives on His Sabbath Exo20:11 and blesses the man who keeps it Isa56:2 that no man can take away what God blessed Num23:20 they will sadly just forfeit their own Psa37:22
Gal 3:26 For you are all sons of God through faith in Christ Jesus. 27 For as many of you as were baptized into Christ have put on Christ. 28 There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus. 29;And if you are Christ’s, then you are Abraham’s seed, and heirs according to the promise.
So the same promises made through Abraham we receive through faith. Why God's only covenant that remembers our sins no more is still with Israel, we enter through faith and in by doing so have God's laws written in our minds to know and do them and written in our hearts because we love Him so much and want do what He asks John14:15-18 sadly not everyone is in this covenant because they have rejected the terms - they won't subject themselves to His laws Rom 8:7-8 - no one is sealed by the Holy Spirit by being in rebellion to God and His commandments 1John2:4 Heb 10:26-30 - He invites everyone to join themselves to the LORD to be His servant Isa56:6 not everyone responds to His invitation.
I hope you meant "the only covenant that God remembers our sins no more is with [SPIRITUAL] Israel" (Rom. 2:28-29, 4:16-18, Gal. 3:28).
With this amendment, the rest of your post is agreeable.