censorship, by definition, is a government activity

No it isn't. "Censorship" is the suppression of speech, public communication, or any other information. It doesn't matter who does it, or whether it is justified or not, it is still censorship. That is why we can have

• government censorship;
• private censorship (question the official line on Covid vaccines or say that people with penises are not women? Twitter will ban you);
• academic censorship (challenge the so-called "liberal" establishment narratives in college, and see your job go bye-bye);
• parental censorship (internet Nannyware);
• self-censorship (when is the last time you told your boss exactly what you think of him?)

etc. They're all different forms of censorship, whether the government is involved or not.

The so-called "liberal" left is subcontracting out censorship to private companies like Twitter (which is why they went insane when Elon Musk bought control of it) and the mainstream media. The government doesn't need to censor when they can leave it to private industry.