EU countries still have:
- their own laws and constitutions
- their own foreign policy, embassies, intelligence services, armies, etc.
- their own taxation; there actually is no EU tax (though there is some pressure to create such a thing)
- their own policies for education, healthcare, social security, taxation, trade, etc.
- their own currency in some cases (e.g. Denmark, Sweden, Poland and many other eastern European countries)
- border disputes like Cyprus, the Balkans (several former Yugoslav countries are members or aspiring to be). And though not part of it, you might count Greenland here as it is Danish with a special status.
As a trade block, the EU is pretty large. And the sphere of influence also includes former soviet states not part of the EU, Turkey, Northern Africa, etc. But it doesn't speak with one voice like the US and China tend to do. Also there is a lot of division on topics like e.g. the Ukraine war, energy, and a lot of other topics.
