There is a line in "Don't Be Fools, America" that I had wondered at: Екатерина, ты была не права. "Catherine, you were wrong" Apparently George had written Catherine for troops to send to the colonies, and at first she (or her rep) had agreed (what uppity subjects!) but then none were never sent. So the colonists got support (of omission in this case, not commission) even from an absolutist monarch because they were…
I think this is a little fanciful, the song is entirely about Alaska which was sold to the US 71 years after Catherine died. The more reasonable explanation is that the line in the song is just wrong for poetic license or other reasons.
which is exactly why I believe it was due to her lack of support during the revolution. Why invent poetic reasons when we already have historical?
https://usrussiarelations.org/2/timeline/first-contact/7
https://usrussiarelations.org/2/timeline/first-contact/8
(TIL there was even support of commission; note that Catherine explicitly cites France as part of her rationale)