Texas Bill to Filter Highway Rest Stop Internet
If I publish a webpage and the state of Texas tells people that they are forbidden from using government-funded equipment to read my document because the state finds the content of my speech to be offensive, the state has abridged by First Amendment rights.
That is both false and not relevent to what we were discussing.
See the supreme court decision about filters in libraries.
And it's irrelevant because they have not made any claim about the blocked content being offensive. Read the bill.
Your sequence of steps fails at step two where they impose a restriction on what someone else can distribute. That is censorship.