The members of the EU are countries, not states (& the EU itself is a political/economic alliance, not a country).
It is common to refer to the members of the EU as "member states."
I'm curious what state you're from where it's normal to refer to EU members as "member states" ? USA perhaps ?
Definition from wikitionary (but nothing is special about this choice of dictionary, you should find a similar definition in any dictionary): https://en.wiktionary.org/wiki/state#Noun
> The European Union (EU) is a supranational political and economic union of 27 member states that are located primarily in Europe.
"State" made perfect sense in context of the post.