It does protect publicly sharing pay. I can't find the specific case at the moment, but there was a case where workers who were striking had printed up a leaflet with a bunch of salary information and distributed it to other workers and general public. The company tried to terminate those employees for violating company policy and sharing "confidential" information with people in the public, but the court found this was a violation of their collective bargaining rights.

It is a tricky issue though. I am sure that a powerful enough company that wanted to throw resources at it could make all sorts of arguments about whether certain parts of the information (e.g. bonuses, vesting schedules, options grants, stock price discounts, relocation provisions) are allowed to be classified as confidential even if basic salary is not.

As a lowly employee, your only hope would be if some national labor union or pro bono legal institute took on your case, otherwise you'd never be able to afford the legal costs to defend your NLRB collective bargaining rights.

With pay secrecy, it's unfortunately still mostly a "might makes right" situation, where rich companies can sort of make up their own rules and at the very least bankrupt you with legal nonsense even if they don't ultimately win. So few people have the fortitude to endure that kind of legal harassment that it implicitly still does censor our ability to talk about pay, even if it's illegal that this is so.