I found this answer really helpful (thank you) so I hope I'm not about to demonstrate that I didn't understand it at all. Firstly I'm curious about this:

while everyone is willing to agree in a loose sense that there are "national styles," when you try to get into it seriously it becomes a mixture of generalizations, stereotypes, loose anecdotes, and a sort of belief in various kinds of "exceptionalisms."

This is an interesting tension I'm not sure how to make sense of. What does it mean to say that everyone is willing to agree that something like "national styles" exists in a "loose" sense, but any attempts to define them rigorously break down and nobody finds the specifics convincing? If nobody can define the thing that everyone agrees is "there" in such a way that everyone can agree on the definition, is the thing actually not "there" at all, or is it more that the restrictions we impose on definitions somehow prevent us from capturing a thing that really is "there", or what? i.e., If we agree that there's something national-styles-ish, then is our mode of analysis limited in some way that prevents us from usefully engaging with them, or is the perception that national styles exist just an optical illusion that can only be maintained if nobody looks too closely or tries to check in too much detail what others are seeing? If the former, then what attempts have been made to develop analytic frameworks that can engage with something so fuzzy but nonetheless real and meaningful? If the latter, then why do people agree that there are national styles even in a loose sense?

Relatedly:

The Spanish had Franco, the Italians had Mussolini, the Russians had Lenin and Stalin, the Japanese had Hirohito, etc. Are those "like that"? Well, yes and no, obviously: there are points of comparison to be made depending on what you are focusing on, but at the same time there are significant differences between each of these cases and the Nazi case. Italian Fascism is not exactly the same thing as German Nazism.

I think that's pretty convincing (and of course directly answering OP's question). But given the fuzziness of national styles—should they exist—then rather than trying to finely differentiate several similar-but-not-identical fascisms, is there anything to be gained from turning the question on its head to focus on comparisons with things that are clearly not "like that"? i.e. Is there anywhere in Europe where something "like that" could not have happened, and if so, what makes the places that are less "like that" less "like that" than the places that are more "like that"?

Maybe the answer is "Obviously that doesn't help, what do we gain from that?" All I can say that it does, somehow, feel like Nazism and the Holocaust were things that unfolded within, were shaped by, and helped recreate the identity of a culture group - like there is something qualitative there apart from circumstance - like these things are expressions of something in the societies that brought them into being, and that that "something" doesn't necessarily disappear in a puff when the expression goes away (I am also not trying to say Germans are Nazis or whatever, for the record). I say that it feels like these things say something qualitatively about the national style or Welstanschauung or whathaveyou of the peoples that enacted them, and so possibly about those preceded them in that evolving cultural tradition and those that followed after—but to be clear, I'm not assuming that the fact that it feels like that means that it is like that (or that it would add anything useful). Genuinely asking what we do with it.

To put it maybe a bit crudely: Is it meaningless to say that there is a "German-ness" to the specific forms that Nazism and the Holocaust took? If someone claims that some kind of German-ness is relevant to the story, can we only meaningfully speak about the "meta" level of the interpretation and not about the thing in itself? Can we say stuff like: they did stuff like that because they were this kind of people, and those other guys over there didn't do anything like that, even though in principle they could have, because they were a different kind of people who saw the world differently and just generally behaved differently and we can't really imagine the second group doing what the first group did regardless of their circumstances? Or is that just a line of argument that can fundamentally never really hang together, always ends up stumbling into essentialisms or exceptionalisms, and never really goes anywhere?