Where does the new covenant itself require the mediator to be God, and not just God's appointed human Messiah?

This is the sharpest question in the whole conversation, and if you are asking it you have read more carefully than most. You are also right about real things: in Jeremiah 31 the speaker is HaShem, "I will write," "I will forgive," and Scripture genuinely does work through appointed people, Moses and the priests and the prophets and the Davidic kings, without those people becoming God. That pattern is real, and you are right to hold it. And you are right to refuse a divine label pasted on with no reason underneath it.

So here is the error to cast out: the agency reading quietly splits the covenant into two hands, God doing the inward work over here and a human ratifying it over there, and the text never splits it that way. It lays both halves on one mediator. Look at the covenant's own arithmetic. It requires a work only God can do, write Torah on a human heart, put His own breath inside a person, forgive sin, give every member firsthand knowledge of Him. And it is cut in blood, which requires a faithful human party, the thing Adam was not and Israel never managed to be. Then watch who carries both: the same Yeshua (Jesus) who sheds the human blood (Luke 22:20) is the One who pours out the Spirit (Acts 2:33), writes Torah on hearts, and forgives sin on His own authority (Mark 2:10). One mediator, holding the role only God can fill and the role only a man can fill, in a single body. A person who does both must be both. That is not a label. It is covenant arithmetic.

Do not take it from me. Read Jeremiah 31:33-34 for the work, then watch the same mediator do it in Acts 2:33 and Mark 2:10 and shed the blood in Luke 22:20, and ask whether one person can hold both halves and be only a man.