Justice Clarence Thomas has called for "revisiting" New York Times v. Sullivan, which "incorporated" the First Amendment to the states, through the 14th Amendment, because by its language it applies only to Congress: "Congress shall make no law ..." Other rights amendments are not thus limited.
As written, the First Amendment was indeed restricted to Congress: “Congress shall make no law …” That led some judges to leap to the wrong conclusion that none of the rights in the Bill of Rights apply to the states, in the case of Barron v. Baltimore. The 14th Amendment was largely to reverse that precedent, and all others built on it. But that led to the Slaughterhouse Cases, which, in dictum, not in edict, deprecated the “privileges oe immunities” clause of the 14th, which, properly understood, incorporates all of the Bill of Rights to the states. Since then, the Supreme Court has been selectively “incorporating” some but not all of the Bill of Rights to the states.
The break in this process came in Griswold v. Connecticut, which incorporated the Ninth Amendment, with all its “unenumerated” rights, which includes all the other rights, including those of the First Amendment.
The issue in Sullivan was not attempts of a state to legislatively restrict news outlets, or the content of their reporting. It was state libel laws that made it too easy to sue for libel. The case raised the standard for such cases to prove "actual "malice". In other words, not only stating an untruth, but do do knowing it is untrue, with the intent to injure. That is usually difficult to prove, against a defense that it was a careless error. The standard can also be applied to verbal libel (slander), if the target is a public figure.
So the Court in Sullivan erred in its reasoning. The right they wanted to incorporate was not the First, but the Ninth. Justice Clarence Thomas has recently raised the issue, saying the Sullivan case should be “revisited”. He did not specify how he would do that.
Keep in mind that when the First Amendment was drafted, some states did have “established” religions and the restriction to Congress was intended to avoid rejection of the Bill of Rights on such grounds. Unfortunately, the rights to speech, press, and petition were thrown in. So the intent of Sullivan should be understood as a Ninth Amendment” case, not a “First Amendment“ case.
See Revisiting 'New York Times Co. V. Sullivan' for further discussion.