That's not what censorship means. Actual censorship, which was seen in Eastern and Central Europe and some other places during communism meant that you're literally not allowed to say certain things. You'd be prosecuted by the government if someone reported you or the government found out in any way that you were spreading certain kind of "forbidden" ideas. It didn't matter where you said it, when you said it, to how many people you said it, and if you used your own platform to say it or someone else's. It was simply not allowed.
What Americans call censorship is not that. Anyone who is banned from a particular platform still has freedom of speech. They can say whatever they want to whoever they want without the fear of government prosecution. If Twitter bans someone, it doesn't mean that the banned person can't speak somewhere else. Everyone has a right to moderate their private property which includes digital space. Although banned from Twitter and some other platforms, Trump didn't lose his freedom of speech. He can say whatever he wants. It's just that he will need an alternative way to reach a big audience because major companies specializing in providing big audiences don't want to provide him their services.
This seems like a fairly antiquated view that does not map well to the current era or actual definition of censorship (A cursory internet search will help to better inform you as to what censorship entails and what actions may reside within the purview of censorship).
One does not have to prosecuted by the government in order to have their speech censored, access to a public forum revoked, or have their livelihood and career threatened.
There are things you simply cannot say within our society due the fact that they are deemed subversive or improper. This arbitrary ability to ascribe these labels to speech and thereby limit its reach and punish those who speak it is the very abuse of power that is characterized as "censorship".
A government is one institution that concentrates power that can be a censor, but in modern times there are alternative organizational structures that are both powerful and global that can perform the act of "censorship".
> This seems like a fairly antiquated view that does not map well to the current era
It very well could be. I grew up in Croatia, I was born right after Yugoslavia fell apart together with its communist regime, so I might be biased towards what I've heard about those times from older members of my family, my history classes, interaction with peers from both Croatia and other ex-communist countries in Europe through youth exchanges, etc, although I was lucky enough to be born in the right time to not live during that period. I'm pretty sure that my views on censorship, free markets, government intervetion, etc. were shaped by my environment. So every time that I read someone claiming that what we see in the US right now is censorship what comes to my mind is that people in Europe during communism would be happy if if was like that during their times.
Well it is also important to note that censorship is a continuous variable. Censorship can gradually increase over time, and what many people in the US are observing is that even in the absence of any censorship (Note: I do not think there is an absence of censorship), the mechanisms for application of censorship are becoming evermore potent.
Think of it in the language of physics. Regardless of the "Kinetic Energy" of censorship, the "Potential Energy" for censorship in is the US with concentrated power to decide who can say what and effectively remove people from public life and discourse is likely far greater than existed in a country like Croatia (which you believe to have had far greater "Kinetic Energy" than the US has).
What Americans call censorship is not that. Anyone who is banned from a particular platform still has freedom of speech. They can say whatever they want to whoever they want without the fear of government prosecution. If Twitter bans someone, it doesn't mean that the banned person can't speak somewhere else. Everyone has a right to moderate their private property which includes digital space. Although banned from Twitter and some other platforms, Trump didn't lose his freedom of speech. He can say whatever he wants. It's just that he will need an alternative way to reach a big audience because major companies specializing in providing big audiences don't want to provide him their services.