> The member countries are sovereign and obviously can't go against their constitutions or basic laws

False.

> The principle was derived from an interpretation of the European Court of Justice, which ruled that European law has priority over any contravening national law, including the constitution of a member state itself.

https://en.wikipedia.org/wiki/Primacy_of_European_Union_law

Mm.

That is sort of like a supremacy clause, and of course it's valid for the EU.

But that doesn't mean that a Swedish or German etc. court can let that override our basic law. Our basic law is after all the foundation of our law, so if something conflicts with that, it obviously can't be valid.