Free speech is the guarantee the government won't censor you. Just because Twitter shares are tradable on public markets doesn't mean they're a public utility.
Musk made his comments in context of social networks. In a digitizing world where all conversation is centered into a handful of platforms, those platforms become the free speech carrier, no matter who owns them.
Yes, you're technically correct, but it's irrelevant from a pragmatic point of view. A legal definition of free speech is worthless if said free speech cannot be expressed in the places where most speech happens.
You can argue that major platforms like Twitter are essential to free speech, maybe even persuasively. What you can't do is make your case as if it were a self-evident fact. It is not.