The big one in the USA is the National Labor Relations Act, but this generally applies to group action. However, such group action can be literally publically posting about a job's work conditions.
Here's a list of recent state laws in Washington, Oregon, and Maine, which prohibition certain kinds of NDAs (oriented toward unlawful activity, not general speech rights): https://www.foley.com/en/insights/publications/2022/07/sever...
Contracts are required to be 'reasonable' for both parties. This puts limits on the ability to constrain in a contract. I don't know how much this reasonableness standard is statutory or judicial.
For public-sector employees there's some protection under the first amendment. https://www.workplacefairness.org/retaliation-public-employe...
And in Connecticut this free speech protection transfers to private-sector employees too: https://law.justia.com/codes/connecticut/2005/title31/sec31-...
https://www.natlawreview.com/article/free-speech-and-express...
https://www.pullcom.com/working-together/there-are-limits-to...
> there is no statutory protection if the employee was only complaining about personal matters, such as the terms or conditions of employment. The employee has to show that he was commenting on a matter of public concern, rather than attempting to resolve a private dispute with the employer.