Well there are not. And they did relinquish sovereignty on borders: Schengen means you do not control your border and we've seen exactly that over the years. This is factual, not an opinion. Even just free movement is a big reduction of sovereign border control and certainly of immigration (in effect you no longer have control of that). We can discuss the pros and cons but not the facts.
Yes they are, they are checking IDs are borders again.