White House's exact words were "we're flagging problematic posts FOR Facebook that spread disinformation". "FOR" is an important word.
https://caitlinjohnstone.substack.com/p/biden-administration...
On top of this, they have already threatened the companies during the hearings that if they don't take it down, then they will get actioned. Plus Biden even called social media companies murderers.
"Congressional Democrats have repeatedly made explicit threats to social-media giants if they failed to censor speech those lawmakers disfavored. In April 2019, Louisiana Rep. Cedric Richmond warned Facebook and Google that they had “better” restrict what he and his colleagues saw as harmful content or face regulation: “We’re going to make it swift, we’re going to make it strong, and we’re going to hold them very accountable.” New York Rep. Jerrold Nadler added: “Let’s see what happens by just pressuring them.”"
This is literally what makes them state actors. I don't know what more they need to do for you to prove they are state actors. There's also precedent from Supreme Court.
"For more than half a century courts have held that governmental threats can turn private conduct into state action. In Bantam Books v. Sullivan (1963), the Supreme Court found a First Amendment violation when a private bookseller stopped selling works state officials deemed “objectionable” after they sent him a veiled threat of prosecution. In Carlin Communications v. Mountain States Telephone & Telegraph Co. (1987), the Ninth U.S. Circuit Court of Appeals found state action when an official induced a telephone company to stop carrying offensive content, again by threat of prosecution."
"As the Second Circuit held in Hammerhead Enterprises v. Brezenoff (1983), the test is whether “comments of a government official can reasonably be interpreted as intimating that some form of punishment or adverse regulatory action will follow the failure to accede to the official’s request.” Mr. Richmond’s comments, along with many others, easily meet that test. Notably, the Ninth Circuit held it didn’t matter whether the threats were the “real motivating force” behind the private party’s conduct; state action exists even if he “would have acted as he did independently.”
https://www.wsj.com/articles/save-the-constitution-from-big-...
Bantam Books v. Sullivan (1963):
https://www.mtsu.edu/first-amendment/article/378/bantam-book...
Carlin Communications v. Mountain States Telephone & Telegraph Co. (1987):
https://openjurist.org/827/f2d/1291/carlin-communications-in...