If I remember correctly, there’s something about this in the OT before King David is appointed. God expresses concern that monarchy becomes idolatry and the people forget their covenant is actually with God, not a fellow mortal claiming to be ‘special’. However, monarchy has its symbolic uses to God, so it’s permissible on conditions of divine authority.
God has always been symbolic, rarely literal. I’d argue the symbolic connection remains between God and monarchy (constitutional or otherwise).
The symbolism of the Crown is that the monarch is saying they’re Head of State, but that God is above them and their Head. Divine appointment etc.
Monarchy without God is harder to justify. Yet so many people don’t believe in God, especially when compared to the last coronation, 70 years ago.
God comes in the monarchy package deal. Tough luck…
You can not have a monarchy without God in the picture - AIBU