European Union is not a federal government like the USA but a union of independent countries.
In Europe it’s normal to live your entire life in the country you were born. Of course you can move wherever you want whenever you want but it’s never needed because there is 99% odds that your state have what you need (specific university, companies offices …)
Since Europe have really poor democratic control and power structure as of today, we are far from a federal Europe.
Even European policies like RGPD are always enforced locally at country level, there is no such thing as European government.