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So - it may be just a result of them being a populist party.

As far as I can see it, this is spreading.

Regarding the source, here is one I was thinking about earlier:

Eine besagt, daß vor 1933 sowohl im Deutschen Reich als auch in Thüringen für alle Bemühungen der Nazis gerade die kommunale Ebene eine bedeutsame Rolle gespielt hat.

From: https://www.rosalux.de/fileadmin/ls_thueringen/2007_Wei%C3%9Fbecker_Kommunalpolitik_NSDAP.pdf page 2.

Regarding the remaining part of your reply:
It seems that you understand Nazis in a form when they were already at a state of having considerable amount of power. I understand Nazis already on a mere ideological level, that's why I see a lot of similarities between Nazis back then when they were just starting out, and those Neo-Nazis now who come in several colours and shapes. And especially the AfD seems to be a magnet for those extremists.

“Antisemitic and xenophobic” statements are not limited to Nazis

Yes of course not. This is just another exemplary piece of the whole image.

I don’t think they’ve started killing their opponents on the streets yet, or forming paramilitary groups.

As I said before, they haven't reached that level of power yet. Besides that:
The politician Wolfgang Lübcke was killed by a right-wing extremist who had ties to the AfD. Even though - in all macabre "fairness" - the party is not responsible for that, this again shows a severe lack of distancing from right-wing extremism within the party.
Then there is the "Reichsbürger" (citizen of the Reich) milieu, against whom police raids were conducted where plans to overthrow the government were revealed and a over 100 weapons were confiscated. This is not the AfD, yes. But here again, a lot of AfD members seem to tolerate or even downplay this (see for example this article). And let's not forget how a AfD politician gave tours to Reichsbürger-members through the government disctrict in preparation of them planning to storm the Bundestag.
Even (former) AfD members criticize their (former) party and make comparisons with the NSDAP, like a former AfD city councillor.

Let's deal with this here:

They speak like Nazis,

Not really

Oh boy, I can give you many many many examples. But let's take one promiment one, since I've already written a lot: The floor leader of the AfD Thuringia, Björn Höcke, got his immunity lifted several times and against whom a criminal process is currently running for demagoguery and using the SA (Sturmabteilung of the NSDAP) slogan "Alles für Deutschland". (Since there are several articles about that and is also listed on wikipedia, you can easily find according sources yourself, but I'll leave you one article on that here for your convenience: Björn Höckes Immunität erneut aufgehoben .) There is so much more regarding his views and what he said, which makes it hard for me to not see him as a Nazi.

Nazis in other parts of the world usually were pretty open about their intentions from the very beginning, while AfD doesn’t send the same signals

Maybe a slightly deeper dive into AfD talk might change your mind ( https://www.youtube.com/watch?v=--UWifFi978 https://www.youtube.com/watch?v=2YCScM7qd8g ). That's were our experiences seem to differ. It's a slow process, but there are many problematic signals (and as time goes on we get more and more of them) which show that the AfD are becoming a serious problem if they don't start to fight against extremists within their own party. The NSDAP didn't start sterilizing disabled people from day one either.