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It's a project whose intended audience is the EU, with (hopeful) eventual EU adoption.

It seems not worse than e.g an American activist labeling their initiative "The American ________ Project". It's perhaps misleading here because HN's (otherwise good) rules to prevent sensationalism in titles disallows the poster to contextualize a post, except in a comment.

The project is led by EU citizens. Do you want a stamp from the European Commission to call it "trully European"? (If so, I would object).

Is EU copyrighted?

"EU" is below the threshold of originality; it is not possible to "copyright" two letters, especially without any font or design associated with them.

Perhaps you are instead thinking of trademark protection? Trademark protection, of course, protects trademarks for particular specified industries and is scoped to nations where the holder does business/exists/has jurisdiction.

It's unlikely this will help, but it's 100% certain that copyright ain't gonna apply.

1) You are confusing copyright and trade marks.

2) Is "American" (or "Chinese", etc.) trademarked?