“The oral law was also given to Moshe. The written law is essentially the headnotes. It’s not the complete law.”
Hogwash. Even if that were true, that oral law would have been completely lost to the Jews long, long ago, so the “oral law” that you have today could not possibly be the same. Don’t you remember, even the written law was forgetten by the unfaithful Israelites until they rediscovered the Book of the Law in the Ark of the Covenant?
So, if they didn’t bother to preserve the written law, then there is no way that they preserved some “oral law” from the time of Moses.
The oral law was written down in the Talmud, and was followed and cited by the Nazarine preacher many claim is the mosiach.