Don't want to give the impression from previous post that I am some sort of scriptural fundamentalist. Far from it. The O'Donovan book is a study of Biblical concepts of political authority. Not sure that I agree with him, but the investigation itself is of interest to me.
The argument that structures of government and political authority, if they are sustained and legitimate, are evidence of divine providence, are the working out of history as a divine narrative - well, this is very questionable...
I'm more inclined to think that, assuming the existence of God, human nature has been endowed by same with natural capacity for government - and that this, itself, is the fact of providence, its basic expression. Humanity, through ignorance and sin, is capable of practicing injustice and oppression, rather than justice and good government. Bad government (or no government) can take various forms of anarchy, tyranny, aggression, etc. The existence of any particular established government is not necessarily an expression of God's will, as far as I can see. But that humanity has been endowed with the potential to recognize and value justice, equity, equality, peace - and the ability to work cooperatively with others to establish same - this seems like the first principle of "providence".
I don't know enough philosophy or political theory to be able to say what are the historical origins of this perspective. Maybe it's "natural law" theory of some kind. Aristotle : "man is the political animal". Dante : "man is the companionable [social] animal". The pivotal factor is that this is a universal human capability or potential. We are talking about mankind per se.
To assert this is not to deny, to any degree, the functions of revealed religion (and not just Biblical), revelation, or the intervention of the divine in human affairs. I am not arguing for clockmaker Deism. Rather I am suggesting that the prophetic direction of Biblical "providence" is toward the universal (or international) recognition of inherent values already instilled in human nature and earthly existence.
For the time being, anyway, as I investigate these matters, I remain a proponent of Roger Williams' essential contribution - separation of church and state. His insights remain highly relevant. He had a kind of magnanimity of thought : recognizing "civic virtue" was not, as the Puritans had it, a consequence of following the letter of Old Testament instructions, but was inherent in the common sense, and innate awareness of right, which were in evidence (partially) in all kinds of societies - Christian, Muslim, pagan, Native American... For Williams, basically, all earthly government was mortal, corrupt, fell short - Christian government included. The difference between the "two tablets" of the Mosaic Law, for Williams, symbolized the division between spiritual worship and civil order. Spiritual worship of God was a matter of individual freedom of conscience - impossible to impose by social pressure or government decree, because the personal discipline of spiritual worship, and the searchings of the individual conscience, were simply too difficult to impose or to follow "on command". They were between God and the person - and any social or political interference with same was out of order.