Couldn’t the argument already be made that by their actions of censoring and Fact Checking and Misleading notices... is in and of itself Publishing, and the Immunity Clause DOES NOT APPLY Anymore???
The courts have ruled for them a few times so no... It needs legislation,
I’m guessing that this is a preliminary, rather mild effort.
It will fail.
Then a more serious effort will be made. The Executive branch should have great power in this area. If the House won’t act, then the FCC or other body will.