As I feel like having to point out every single time this is mentioned because I know exactly how people try to relativize this:
Yes, he tried to use plausible deniability by talking about how "his heart goes out" to people right before doing this gesture, but you know exactly what this looks like and you know that this is not a gesture commonly used to express that sentiment anywhere in any cultural context that would explain this.
This means there are exactly two scenarios in which this is not intended to be a Nazi salute:
1) Elon Musk is incredibly unaware and despite Twitter (including his replies) being overrun by people blatantly Nazi-posting (as in, literally posting videos of the Third Reich or Adolf Hitler and expressing admiration for that era and its sentiments) and him himself having made "jokes" before that suggest sufficient awareness to recognize this gesture for what it looks like - SOMEHOW he is gormless enough to have come up with a gesture that completely by accident unintentionally looks like a Nazi salute and used it multiple times without realizing what it looked like.
2) He's just as gormless as in the first scenario but did realize what it looked like and didn't think that's worth apologizing for and instead doubled down by making fun of those calling him out for it.
But even in those two scenarios he is clearly okay with people (especially the far right) thinking that's what he did and doesn't feel like it's worth distancing himself from those who think that's a good thing.
So in other words, either he did a Nazi salute or he is okay with people thinking he did a Nazi salute. Those are functionally and consequentially identical outside the brain of Elon Musk himself.
Personally I think - given how obsessed he is with extremely stale and tired memes and low-effort shitposts - he wanted to do a Nazi salute but also wanted to maintain the thinnest of pretenses that he didn't, just in case it might come back to bite him. He saw that he got away with it and decided to double down in order to mask his insecurity.
And no, those pictures of Democrats holding their hand at a similar angle don't demonstrate anything and anyone who posts them is fully aware of that. This isn't just him deciding to do a weird greeting and ending up in a position that looked awkward, this is him deciding to do a full, forceful motion that could not have looked any other way no matter the angle - and then repeating it to provide a second look from a different angle to eliminate all doubt to what he did. There's only one clip of a US politician or media figure who isn't an open Nazi doing a salute like this I have seen and it's from a Republican who quickly chickens out by waving at an awkward angle - and that's still offering far more plausible deniability because she only did it once.