Social media companies have some leeway to censor users on their own due to the way the courts have interpreted section 230 of the Communications Decency Act, but if that is in any way coordinated or coerced by government, that makes the social media company an agent of the government and a direct violation of First Amendment protections.
Attorney General of Missouri Eric Schmitt as well as the AG of Louisiana Jeff Landry have filed suit citing collusion between dozens of Biden Administration officials colluding with social media to censor people, including naming accounts they wanted banned or shadow banned.
Upon discovering how wide spread the collusion is, the state attorney generals have asked the court for more discovery to see just how far it goes and the court has granted their motion.. The Biden Administration is not happy, but this court takes the First Amendment seriously.
Attorney Robert Gouveia gives an excellent analysis of how how far this has gone as well as an explanation of the court filings: