The question was: How does it fit in? Because the government is involving itself in actions of censorship, even if it is one step removed.
Similar to how I can still be accused and convicted of a crime, if the only thing I did was facilitating it? I'm not a lawyer, but I hope I'm getting my point across here.
The First Amendment generally only applies to governments. If companies exert government powers--company towns are the canonical example here--it can apply to them, but only to the extent that they are exerting such powers. The other way you can get state action is if there is some degree of government coercion (essentially, you have to be unable to say "no" to a request).
There are some colorable arguments that the government has exerted such coercion over Twitter et al in recent years, but I have never seen a lawsuit alleging such a connection that properly made those arguments, as those people instead prefer to make cockamamie theories such as "§230 makes everybody state actors."
The question was: How does it fit in? Because the government is involving itself in actions of censorship, even if it is one step removed.
Similar to how I can still be accused and convicted of a crime, if the only thing I did was facilitating it? I'm not a lawyer, but I hope I'm getting my point across here.