It didn't. But Israel was to be an example to other nations about how to live.
These "spiritual laws that that God had included in the Sinai Covenant, that 'would be written in the heart"; where does it ever say that the laws that God will write on the heart are the the same laws of the Sinai Covenant, and that they include such things as new moons?
What about the new moons? Can you be specific?
1 Chronicles 23
30 They were also to stand every morning to thank and praise the LORD. They were to do the same in the evening 31 and whenever burnt offerings were presented to the LORD on Sabbaths and at New Moon festivals and at appointed feasts. They were to serve before the LORD regularly in the proper number and in the way prescribed for them.
2 Chronicles 2:4
4 Now I am about to build a temple for the Name of the LORD my God and to dedicate it to him for burning fragrant incense before him, for setting out the consecrated bread regularly, and for making burnt offerings every morning and evening and on Sabbaths and New Moons and at the appointed feasts of the LORD our God. This is a lasting ordinance for Israel.
2 Chronicles 8:13
13 according to the daily requirement for offerings commanded by Moses for Sabbaths, New Moons and the three annual feasts—the Feast of Unleavened Bread, the Feast of Weeks and the Feast of Tabernacles.
2 Chronicles 31:3
3 The king contributed from his own possessions for the morning and evening burnt offerings and for the burnt offerings on the Sabbaths, New Moons and appointed feasts as written in the Law of the LORD.
Nehemiah 10:33
33 for the bread set out on the table; for the regular grain offerings and burnt offerings; for the offerings on the Sabbaths, New Moon festivals and appointed feasts; for the holy offerings; for sin offerings to make atonement for Israel; and for all the duties of the house of our God.
Cordially,