The EU project has always been a project rather paternalistically cultivated by US foreign operations, including intelligence operations, so I believe.
It allowed them to remove a heap of troops from forward bases in the region.
The CIA has certainly done some regrettable/shady stuff historically, as have almost all intelligence organisations that I’m aware of (reading about the history of espionage and covert activities, I often wonder how the people involved manage to preserve any sort of sanity in that mistrustful, cloak and dagger world?).
Although politically (and somewhat culturally?) natural allies, being that both entities are largely a collection of democracies/republics, if you view global economics as a zero-sum game you could say that the EU is a direct competitor to the US.
Indeed, although politically less-strongly federated/bound together, as far as I’m aware, the EU has greater wealth as a whole than the US does. Various governments, companies and individuals that oppose democratic forms of government and ‘liberal’ values see the economic strength, cooperation and mutual defence/offence promoted by an alignment of these two political organisations as counter to their interests, or potentially a threat to more authoritarian hegemonies. Contrary to what you say, the previous US administration actively supported Brexit. Many authoritarian governments around the world were also cheering it on, as presumably geo-strategically it was/is in their interests to divide and undermine democratic forms of government.