EU member *countries" certainly do, but that's true of all countries that have the ability.

If anything the EU puts limits on what EU member countries and companies can do. By hosting in one of the EU countries you have stronger legal guarantees on data privacy than in any other area. A possible exception is Switzerland (not a EU member), which historically has had even stronger privacy laws, though these have been weakened recently IIRC.

> Does the EU not want to spy on its citizens?

You do not seem to understand what the EU is. It is not a country, it does not have a police or anything like the NSA.

No they don't want to spy. They want to protect their citizens data, that is why we have GDPR. The other areas you mention do not provide this legal certainty and have different approaches to data privacy.