There is not just one ethnic European group, there are many.[1]
I didn't mention the word "race" in any of the comments above. However, scientists show us that different groups of people on Earth cluster together genetically closer than they do to other groups of people. [2] This is what one expects if the ancestors of these groups parted ways millennia ago. What you mention about Turks and Greeks is not unexpected, Greece and Turkey being practically next to each other, I don't know why you bring this up.
You are entirely correct about pre-modern European tribes and nation states. If the comment above implies something different from this although I believe it doesn't, then I made a mistake.
We moved to the concept of "race" about which you are absolutely correct. It's a sociopolitical construct and the meaning of this word has not been consistent throughout history. Remember though that I didn't use this word.
Back to the genetic argument, why doesn't the projection matter? (argument b) which grand-parent was justifying)