New covenant purpose

I was brought back to the faith by reading the New Covenant prophecy of Jer 31, as quoted in Heb 8 & 10. Catholics, do we understand these central teachings?

Jer 31:33-34:
“I will put my law in their minds
and write it on their hearts.
I will be their God,
and they will be my people.
No longer will they teach their neighbor,
or say to one another, ‘Know the Lord,’
because they will all know me,
from the least of them to the greatest,”
declares the Lord.
“For I will forgive their wickedness
and will remember their sins no more.”

The Catechism of the Catholic Church:
1965 The New Law or the Law of the Gospel is the perfection here on earth of the divine law, natural and revealed. It is the work of Christ and is expressed particularly in the Sermon on the Mount. It is also the work of the Holy Spirit and through him it becomes the interior law of charity: "I will establish a New Covenant with the house of Israel. . . . I will put my laws into their hands, and write them on their hearts, and I will be their God, and they shall be my people."19

1962 The Old Law is the first stage of revealed Law. Its moral prescriptions are summed up in the Ten Commandments. The precepts of the Decalogue lay the foundations for the vocation of man fashioned in the image of God; they prohibit what is contrary to the love of God and neighbor and prescribe what is essential to it. The Decalogue is a light offered to the conscience of every man to make God’s call and ways known to him and to protect him against evil:
God wrote on the tables of the Law what men did not read in their hearts.13

1963 According to Christian tradition, the Law [ten commandments] is holy, spiritual, and good,14 yet still imperfect. Like a tutor15 it shows what must be done, but does not of itself give the strength, the grace of the Spirit, to fulfill it. Because of sin, which it cannot remove, it remains a law of bondage. According to St. Paul, its special function is to denounce and disclose sin , which constitutes a “law of concupiscence” in the human heart.16 However, the Law remains the first stage on the way to the kingdom. It prepares and disposes the chosen people and each Christian for conversion and faith in the Savior God. It provides a teaching which endures for ever, like the Word of God.

The Catholic faith is not about obedience of God’s revealed Law first of all, but about communion with God first of all, a relationship that begins with faith in response to grace, to His calling. We need Him in order to be obedient, in order to have the righteousness or justice we were made for. Man was made for communion with God, ‘apart from whom we can do nothing’, paraphrasing John 15:5. The law only tells us what righteousness “looks like” . We need Him to be able to pull it off in us, to justify us, IOW-to produce the love in us that fulfills the law by its nature, to put it another way.

I’m curious if any of this is novel-or just standard-brand Catholic teaching as far as everyone knows?

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