I'm sorry, I'm not 100% sure what you are saking. You haven't seen anything similar to bosses not publishing their employees salary? Or US law protecting the rights of employees in something?

Sorry, I meant explicitly forbidding a supervisor from discussing working conditions or salary with their subordinates is pretty rare in Europe, and in fact that's the only time I've been told of such thing.

I was wondering if that kind of clause is a common thing in the US - for instance limiting job mobility by not allowing you to work for X client for N years is common in Europe, while I get it's rare in the US from what I read on social media / HN.

In the US its rare for a supervisor to divulge what your coworkers are making. It's normally not "forbidden" just not done. Heck, look how antsy some people are at telling other people their salary in this thread. Does your boss tell you what your peers make?

As someone who has worked in a French SSII, and talked with other consultants: it's common here too. The intermediaries want to maintain information asymmetry.