It's is (or was) a common formulation used on government documents such as the U.S. Constitution, the Emancipation Proclamation, various treaties, etc. I don't know if it fell out of favor or was reserved for a limited list of acts.
Personally, I don't read much into it apart from the importance of recalling our founding.
(I don't immediately think of Britain when I think about our independence. I think of the blood shed by patriots to establish limited government of, by, and for the people.)
Second row & a hero @realDonaldTrump πΊπΈ pic.twitter.com/bxdQJg7XAIβ Kimberly Klacik (@kimKBaltimore) December 6, 2020