You say the New Covenant is not a promise between God and man, but really a promise God made to Himself. Where do we find this in Scripture?
And it was not without an oath! Others became priests without any oath, but He became a priest with an oath when God said to Him
“The Lord has sworn and will not change His mind: “You are a priest forever.” Because of this oath, Jesus has become the guarantee of a better covenant.
Hebrews 7:20-22