More specifically, the theory is that cannot compel you to lie, there are all kinds of cases where businesses are compelled to share specific messages.
As far as I've seen, the examples of that have always been things like health warnings and ingredients lists, where showing that message is a condition of being in that (licensed) business, and applies equally to any company.
For employee things, I can understand being required to notify parties in agreements the company has entered into. As far as I understand, consent degrees are settlements and as such a mutually-agreed mechanism for ending a lawsuit early; their terms are whatever the parties negotiate and do not come from the government.
To be more precise, the law requires employees to publish the nlrb notice in well trafficked or otherwise conspicuous locations.
I think there are other places where "government mandated corporation inform people of their rights" is a thing, especially with things like data use and sharing.
In terms of consent decrees, that was the wrong example. But lots of judgements do involve various notification requirements.
Car manufacturer warranty recall letters are probably a good example.
I get them even though I've never done business with the car manufacturer -- I bought the vehicle from a private party.
But that still sort of connects (at least in my mind) to health warnings etc.
