From the third link, do you believe there are subtle differences between the two gestures that we're missing, or are you saying that Adolf himself failed and delivered a Roman salute instead of a Nazi one?

Ah yes, the Nazi salute's innocuous cousin, totally unrelated to the far right, the Roman Salute... /s

Unfortunately, this isn't a one off connection. For instance, search Musk and the AfD.

Eventually you see enough associations between a person and who he sympathises with and you have to ask some questions.

"throwing his heart out to the masses" is just not a thing. That isn't a gesture people make or that anyone has ever claimed to make before yesterday.

The "roman salute" (which was invented by Italian fascists and not the Romans) is the same thing as the Nazi salute.

A "roman salute" is the fascist salute. The word "fascist" comes from Italian politics and is derived from Latin:

https://en.wikipedia.org/wiki/Italian_fascism

https://en.wikipedia.org/wiki/Fascism

So ultimately you've agreed that Musk did indeed do a fascist salute.