We measure our independence from 1776 in spite of the fighting lasting until the Treaty of Paris in 1783. The British continued to keep fortifications on the Canadian border and even built an additional fort in present day Ohio in 1794. After that, the British invaded the United States and burned Washington DC during the War of 1812 with belligerence continuing until the Treaty of Ghent in 1815. Even after that, disagreements with the United Kingdom along the Continental Divide lasted until the Oregon Treaty was finalized by arbitration in 1872.
So, I suppose it all depends on who is telling the story.
I don’t think the USA had a governor general after 1783, or any allegiance to the British king. Ireland had a governor general until 1931 (abolished by the Statute of Westminster), as well as a requirement for an oath of allegiance to the British king (abolished by De Valera).