You make it sound like there was a Union when Washington was fighting. There wasn’t. In fact, they ended up with a confederacy of independent nations for 9 years until the secret convention where it was proposed to have a federal system, a Union if you will.
The idea of the Union was present in Washington’s writings during the Revolutionary War.
That Confederation turned out to be so inadequate that a new Constitution was deemed necessary. But even under the Articles of Confederation we still had one army and one set of diplomatic representatives. We were, so far as the outside world was concerned, one union and one nation.