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It is also perfectly clear that on July 4, 1776 when the Declaration of Independence was adopted, it was not unanimously agreed to yet and lacked any concurrence from the New York delegation, which was still awaiting instructions.

The first broadside copies of the declaration were printed that evening and did not have the word "unanimous" across the top like the more famous copy. It only became unanimous several days later when New York gave its support. Thus for a period of about a week or so, New York had not consented to independence yet making any "union" that existed at the time split on the issue of breaking away from Britain.

"It is also perfectly clear that on July 4, 1776 when the Declaration of Independence was adopted, it was not unanimously agreed to yet and lacked any concurrence from the New York delegation, which was still awaiting instructions."

Tsk tsk. The New York delegation had been instructed not to vote on an independence declaration. The Colonial legislature provided its approval a few short days later.

Also you error in your understanding of the term "unanimous." New York did not vote against independence. Nor did any other delegation. Therefore, the vote was unanimous. With the New York leglislature's approval, it became the unanimous declaration of all 13 colonies. In the meantime, the New York delegates continued to participate in the Continental Congress (drafting the Articles of Confederation) and New Yorker's in the war of independence. New York was very much a part of the Union - an important part - prior to and after the Declaration. Your argument is silly.