I’m not sure this is correct; in general many people would think of themselves as X and European, where X is the country of origin or citizenship. The EU is not

I’m not sure this is correct; in general many people would think of themselves as X and European, where X is the country of origin or citizenship. The EU is not a country. For that matter, the UK, despite being a country, has some aspects of this; while Northern Ireland in particular is complicated for historical reasons, plenty of English and Scottish and Welsh people would think of themselves as English or Scottish or Welsh AND British.