Aardvark won't answer the question because he can't answer the question. The legal basis for the continental congress, the lawful authority of the team that went and negotiated the Treaty of Paris, all flowed from the claim that Britain lost its sovereign authority through acts that contravened the unalienable rights of the colonists.
In short, the colonists asserted that there was a higher authority than the British sovereign constitutional authority.
They used that authority as the basis to fight a revolution and then to authorize negotiations with the British crown.
That is a political not a legal argument.
As even Nineteenth Century American Historians acknowledged. The Second Continental Congress had no explicit legal authority to govern, however, it took upon itself the functions of a national government. 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.
If you bothered to read books (which you have told us you don’t) you might look at George Bancroft’s
History of America where he made basically the above statement in the third quarter of the Nineteenth Century.
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.
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.
The Declaration of Independence while a wonderful piece of prose was neither the actual vote of the Congress for Independence, nor did it actually achieve it, that was accomplished by British unwillingness to continue a world wide war, when it had become apparent that the genie could not be put back into the bottle.