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.
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."
I would be pretty surprised if this was true but 3rd Party Doctrine is in good standing in 99% of cases.
Edit: Yeah, it appears this is not true at all. The government of course cannot coerce a private company to do this (which is obvious since that'd be tantamount to the government itself doing the censorship), but they absolutely can request it. https://reason.com/volokh/2021/07/19/when-government-urges-p...