Yes, the EU was founded in order to become a country. They were imitating the USA, in which several states united under a federal government, starting off as a loose federation which helped their common interests, and rapidly becoming an all-encompassing overwhelming central power that suppressed the identities of the states.
The EU is trying to suppress the identities of the various countries, and to create an all-powerful central government that suppresses the individual countries. It is well on the way to having achieved that, but now some countries are protesting, since their national identities are being erased.
They still have a chance. They can still get out of the EU and go back to being sovereign countries. They had better do it fast, before the jihadis multiply and take over, establishing a dictatorial theocracy.
Certainly the EU was never imitating the USA as it was founded. It was imitating the elements in the USA that themselves imitated the USSR and who made the UN’s charter a clone of the USSR’s constitution. The words “in accordance with the principles of the Charter of the United Nations” go back to 1957 and the Treaty of Rome.
The EU was founded to be an empire, not a “country”.