Hot take; Greek people are to all intents and purposes Middle Eastern, but have been co-opted into European-ness by white supremacists and other europhiles so that they can claim Ancient Greek culture as their own.
To be more serious, this all points to how whiteness expands or contracts depending on context. E.g. I've seen "white" people in the US who are ethnically Turkish, Lebanese and Syrian. I've also seen Turks, Lebanese and Syrians who are very much not "white."
Only group that has at all times been "white" since whiteness and "race science" were pioneered somewhere around the 1600s are English people of Britain. They pioneered the idea to explain why behavior of the British empire was actually the natural order of things and a just cause.
There were points where pale ass groups like the Irish and Germans weren't white while darker skinned Europeans like the Spanish and Portuguese were. Ofc European nobility were always white even when the commoners of their nations weren't.