That is a political not a legal argument.
It's plainly both.
The Second Continental Congress had no explicit legal authority to govern, however, it took upon itself the functions of a national government.
Correct. It claimed
implicit authority to govern based on the argument advanced in the Declaration of Independence. Namely that the sovereign had lost the authority to govern due by violating unalienable rights. Therefore, in the absence of a proper government, it fell to the local population to formulate a new government, which they did.
Further, each delegation was limited by the instructions it had received from its state. Now you can say that this power flowed from the people or that Royal or Proprietary Governments had lost their authority through acts by the Imperial Government that contravened the unalienable rights of the colonists. The only problem with that is that even John Adams would admit that 2/3 of the people disagreed with such a statement.
Nevertheless that's the argument that was advanced and it's the legal lawful basis of the United States and the source from which all constitutional authority since has flowed.
I agree with you that it flowed through the State legislatures to the Continental Congress, but that's really not material to the point that the authority originated in the claim that the sovereign had lost it.
Even the Revolutionaries most certainly did not in 1775 assert that they were taking up arms in answer to some higher authority (of course except for God) than the British Constitution.
In 1775 they were still hoping that the violations of their unalienable rights could be rectified within the context of British rule. By 1776 they had concluded that was not possible and they drafted the Declaration of Independence.
I really wish that you had a better grasp on this since the Revolution was really at least 13 separate Revolutions more when you ask what was different about Nova Scotia (in part the answer is the "Missing decade"), unfortunately neither UofT nor the University at Buffalo currently offer a course on the Revolution and early Federal periods.
What was different about the northern fishing colonies was that they had a longer history of independence from Britain within the commonwealth. They'd been there since the earliest days, having been initially set up as among the very first permanent European settlements in North America to dry fish for shipment back to Europe. Britain lacked an ample source of salt and so British fishmen plying the Grand Banks had to sun dry their fish in racks on land. Spain, by contrast, had lots of salt, and so their fishermen were able to salt their fish in barrels and did not need to make land fall nor set up colonies. Britain had to set up colonies in order to dry the fish prior to shipment back to Europe and as that could only be done on land they set up colonies early early on to do that.
As the earliest settlements they had to fend for themselves and gained a strong and independent culture early on. Further south there was a much more dependent, integrated relationship with Britain. The consequence is that when Britain came along and tried to impose chartered monopolies and associated taxes on the New World the Nova Scotians and Newfoundlanders were able to say "no", and they made "no" stick. They got an act passed in the British Parliament exempting them from monopolies and taxes on the grounds that they'd been independent from Britain for long enough that they didn't need them.
Thus the resentment that grew in the American colonies over the monopolies and the taxes just didn't happen in what became the Canadian maritime provinces--they simply had less to resent and therefore saw no reason to revolt against British rule.
In any case we're off topic--the topic of the day is the authority of the Americans to throw off British Rule, set up State and Continental legislatures, and rule on their own. That authority derived from their claim that unalienable rights had been violated--it's an implicit claim, not an explicit claim, as it's based on universal self-evident truths and not written law.