Following up on my little test. I tried to register the domain:
testing-eu-registration-from-usa.eu
It went as I suspected, as every domain register that I looked into, asked me to verify my EU Citizenship.
As I stated in my first reply, .EU is not currently available to everyone. I used Domain registers that are outside U.S. Jurisdiction, of course, because you don't want a company within the USA or owned by another USA company. https://codeberg.org/Linux-Is-Best/Outside_US_Jurisdiction/src/branch/main/Web_Hosting.md