https://eh.net/encyclopedia/an-economic-history-of-copyright...
They started allowing non-citizens to get U.S. patents earlier:
"Americans could not obtain patents for imported discoveries, but the earliest statutes of 1793, 1800 and 1832, restricted patent property to citizens or to residents who declared that they intended to become citizens. As such, while an American could not appropriate patent rights to a foreign invention, he could freely use the idea without any need to bear licensing or similar costs that would otherwise have been due if the inventor had been able to obtain a patent in this country. In 1836, the stipulations on citizenship or residency were removed, but were replaced with discriminatory patent fees: foreigners could obtain a patent in the U.S. for a fee of three hundred dollars, or five hundred if they were British. After 1861 patent rights (with the exception of caveats) were available to all applicants on the same basis without regard to nationality."
https://eh.net/encyclopedia/an-economic-history-of-patent-in...
Sam Slater moved to the US in 1789 and partnered with a textile manufacturer to recreate the technology from memory. (Amusingly what he did may not have even been a violation of IP law by today's standards)
https://www.ipwatchdog.com/2017/07/05/americas-industrial-re...
https://en.wikipedia.org/wiki/Samuel_Slater
I think that US publishers, especially sheet music publishers, would copy British music and and publish it in the US, since I don't think that the US honored British copyright (at least some subset of it), but I can't think of good search terms to find any sources.