Unfortunately, what you fail to grasp (at least for the purposes of the arguments in this piece) is that the moral justification for free speech at all does not hinge on whether technically something is provided by a private business or not.
You don't just say, "Well, we need to be able to hold governments accountable for their actions by speaking freely, except our words are conveyed with the help of a company, so who cares, never mind, governments actually don't need to be accountable anymore."
Nor do you say, "A robust contest between ideas is necessary to improve and refine them unless a company touches the process in which case, whatever, any old junk idea will do, who even cares?"
And you certainly don't say, "The ability to govern your own affairs and your own thoughts is central to a good life as a human being, except if an important part of your life is conveyed by a company, in which case, forget all that, it's not important."
So the question is--should Twitter serve this role widely regarded as important (and a critical part of maintaining a democracy)? Because you don't acknowledge fully that a company-provided platform can convey speech, the freedom of which has well-discussed and well-known advantages, you aren't properly engaging with Elon Musk's Twitter-as-town-square position.
Some of the points you make would be good ones if you did acknowledge this. Indeed, I've used most of them myself. But you start off down the wrong path, and thereafter you're arguing a technicality rather than on the ethics of free speech.
Free speech always includes the right to deliver unhelpful and counterproductive speech. But the argument has always been that the institution as a whole is so valuable that the downsides must be put up with. If you eat, you might get poisoned; but you can't do without eating.
What you need to do instead is tackle the moral arguments head-on. I've done as much elsewhere.
Otherwise, you're presenting (apparently) practical issues and setting them against a (presumably) moral issue. The moral issue always wins, at least in the hearts of those who view it as a moral issue.
The trick is that the argument for free speech is not a purely principled one but based on the assumed advantages--advantages which fail to obtain in many social media platforms as currently construed.
That is where Musk's free speech arguments fall flat: they are built upon arguments that take as premises things that are not true of Twitter as it stands. But your arguments also fall flat unless cast in this space, because you're not actually addressing the core issue of the value of free speech.