The language of the criminal provision seems narrow enough to avoid major First Amendment concerns.
It's hard to believe that building a website for unadorned, black-and-white court filings and docket sheets could cost three-quarters of a billion dollars. But that's what the judiciary is claiming it costs.
These bills, or ones very similar, have been introduced in a dozen Congresses over the last two decades. Most recently, they made it out of Committee in 2021; before that, it was 2011.