You are painfully wrong on the definition of censorship. Censorship is the act of a third party intermediary controlling the content of speech, no matter who that third party is. For example, Merriam-Webster defines "censor" as "a person who supervises conduct and morals". They go on to use the word "official, which you might think implies bona fide government. But they define "official" as "one who holds or is invested with an office", which most certainly applies to private corporations.

By banning people based on the content of their speech, Twitter is precisely engaging in censorship. Just because they haven't called their department head responsible for handing out bans a "Censor" does not mean their constructive behavior is something new that we don't have a word for!

Furthermore, immediately referencing the Bill of Rights to call Twitter's activities "freedom of expression" is wantonly destructive to any sort of discussion. The US Bill of Rights takes natural rights and narrowly frames them in terms of restrictions on government, because that is likely the best that can be done at its level of abstraction. The scale Twitter operates at is much closer to that of government than that of the People - it is most certainly appropriate to say that Twitter is impinging upon individuals' freedom of speech. If you do not agree that it is a concern, then go ahead and make that argument on its own merits. Narrowly construing definitions so that you can discard concerns does not make for productive understanding.

(Having said that my own feeling here is that Ms. Ignorance-as-a-Service has reaped what she has sown, is of a notoriety that is legible to Twitter, and can easily publish on other platforms - compare with all the unnoteworthy individuals who get the automated banhammers with no appeal. And this will ultimately just be a boon to her, just like any other celebrity feud. But let us not twist our own definitions to assuage our cognitive dissonance!)