Correct, although I have some regional questions. The "White means European" definition is affected by how Kazakhstan reaches into Europe, how Russia reaches into Asia (Siberia) and by the Ottoman Empire's expansion into continental Europe as well.

These sorts of questions are not relevant to most Europeans. There's always ambiguity around border regions which are resolved (or not) by the peoples living there. We can say with certainty that the modern or semi modern definition of "white" includes almost everyone living in continental Europe.

Even without race science factored in, there is still the whole "x wasn't considered white" component key to whiteness studies which I am currently having questions about right now.

This is mostly overblown modern liberals as a sort of gotchya. "White" is a modern concept developed in contrast (in some cases literally) to other races. European racism against other European "races"/ethnicity doesn't really matter much for the modern definition - most cases of xyz ethnicity not being "white" is really whatever race (in the US case Anglos) seeing other euro ethnicities as "lesser than" rather than "not white" per se. The most notorious example of Irish (and later Italians) in America not being considered "white" was not in a modern racial sense we use nor was it in any way consistent - the mostly English (Anglo-Saxon) derived Southern plantar classes specifically funneled the Irish into the South to help keep it "white" in the antebellum period.

It's very clear from modern genetics that continental Europeans are a very closely related people (in contrast to say African "blacks" which are really a multitude of diverging races with similar phenotypes).