That's just the straightforward stuff. That's without the IRS deciding your corporate profit statements deserve extra scrutiny, and the FCC deciding to question whether you really qualify for section 230, and and and...
You can be right. They can still make your life very difficult if they decide to. And it will be very hard to prove that that's what they're doing. And even if you can, you probably aren't going to get the money back that the court cases cost, and you definitely aren't getting back the time and management attention it cost.
So, not legally coercive. But still kind of coercive, even though legally it has no force.
I mean, yes, you're right, the White House director of digital strategy, taken by himself, can go jump in the lake as far as Facebook or Twitter are concerned. Even given all the people under him, that's still true. The question is, to what degree is he speaking for the people over him? How many layers are there between him and the president? I'd guess somewhere from 0 to 2, though I admit that's a guess. Can he cause trouble on his own? No. But the one giving him orders may be able to give orders to others.
Basically this is arguing that the mere existence of government has a chilling effect, which it demonstrably does, but isn't really something you can make go away with an injunction. Hell, what's stopping the Biden admin from enacting this punishment scheme on these people for getting this injunction?