It doesn’t help that this has been codified into the names of various organizations, like the Council of Europe (ECHR, etc.), EEA, EU, and others that all refer to different subsets of countries on the continent. I suppose this renders any straightforward alternative relatively limited in scope even if a term to refer to one of these memberships was agreed upon.

> Sometimes it is used as the adjective form of EU member state.

Sometimes people make mistakes, sometimes outright errors. Sometimes people use language to push ideas they like, such as "the EU is Europe" and thus not being a part of the EU is somehow an offence against nature. I'm not sure why these mistakes, errors, and mendacities should go unchallenged and uncorrected.

Every use of "Europe" in that article could be replaced with "EU" and it would be the better for it.

Many countries/languages use versions of “The US” and USA to avoid confusing the US with America. So it’s only reasonable that we make the distinction for Europe and the EU.

The problem is the there’s no specific term for the people living in either the US or the EU, so we “wrongly” use Americans and European.

In my experience it's mostly people outside of Europe who confuse the EU with Europe, whereas Europeans are less likely to make that error.