They had their hemisphere long before when they became a colonial power and took that over from the Brits.
Hawaii, Phillipines, etc…
If you live in Europe like myself you might think it was after the cold war since their influence was more noticable here.
We became no more than a glorified colony, something our ‘leaders’ are now feeling but still won’t admit.
Many, including Chomsky have said this and the cold war was actually already the beginning of the decline.
I don’t see an upgrade in ‘soft power’.
That is a precursor to regime change, not an alternative.
They should mind their own business, the new reality of a multipolar world will force them to anyway.