How far out of the public eye does your address have to be? I have filed a few patents and I run a company, and both of those put my address in prominently searchable public records. If you dig a little deeper, the deed to my house is a public record accessible through a 15-year-old website, and going even further, you can do a credit report on me and find all of my past addresses.
I know people wish this weren't the case, but your address isn't exactly private information. Anyone can find it easily for anyone else.
That's true. But if you were to for instance publish that address with a call to action or if you were to compile a list of addresses of politicians with a call to action you'd quickly end up on the wrong side of the law. That is doxing. Merely looking up someone's address used to be a matter of looking in the phone book. And people that did not want to be in the phone book had unlisted numbers.
So the bar for doxing is definitely a low one, but in this particular case it isn't met. I can see why Musk is irritated that that account exists, even more so because it didn't go away at the first request by someone as powerful as him, and that makes it personal. See the whole saga with that diver for a typical response. But that doesn't mean that the person manning that account is doing something illegal and that is the bar which Elon Musk himself set not all that long ago, and which is what makes this news.
If he had been a bit smarter about this he would have just said: "I'm irritated by you, this is my site and you're gone". That would be that. But now there are all these logical pretzels why this is illegal and all that other stuff that people - and Musk - do on twitter is not because 'free speech'. The two are incompatible, and he knows it.
I know people wish this weren't the case, but your address isn't exactly private information. Anyone can find it easily for anyone else.