Twitter is not the government so the First Amendment does not apply to its censorship decisions. Having said that, Elon Musk's ideas about what constitues "free speech" on Twitter strike me as rather arbitrary.
Reporters from the Washington Post, New York Times, and others were banned for sharing publicly available information.
gizmodo.com
The ban on various twitter accounts that were posting publicly available flight tracking information also strikes me as being arbitrary.
>>>Twitter on Wednesday banned several accounts which shared publicly available data on the locations of private jets belong to multiple billionaires, including Twitter CEO Elon Musk who said he was taking legal action against the owner of the accounts for causing harm to his family, another sign that the billionaire has become the singular arbiter of rules on the social platform. . . .
In a separate tweet, the Twitter CEO called the real-time sharing of publicly available flight data—whose broadcast is
mandated by the Federal Aviation Administration— “doxxing” and a “physical safety violation.”<<<
Twitter’s latest rule change comes after Musk blamed the owner of an account tracking his private jet for an alleged attack on a car carrying his young son in Los Angeles.
www.forbes.com
It's hard to see how sharing publicly available, federally mandated, flight data could be "doxing" under any normal definition of the term.
I'm just saying Musk is a Twit ("Twit in Chief"?), not that there's a First Amendment issue.