As Whack-a-Mole pointed out, the polestar of traditional labor law (the law of governing labor organizations and collective bargaining, as distinguished from employment law, which would include things like wage and hour claims or invidious discrimination) is the Wagner Act, which came about in 1935.
What the Wagner Act did, in a nutshell, is to endow labor organizations, workers, and employers with statutory (not constitutional) rights that they did not have before its enactment. In brief, the Wagner Act allowed a labor organization that won a certification election to bargain on behalf of all employees within the certified bargaining unit—including on behalf of those employees who did not want the union certified. It made the certified labor organization the exclusive voice for the bargaining unit employees (see, e.g., Emporium-Capwell, Co. v. Western Addition, 420 U.S. 50 (1975)). It required employers to bargain collectively with the elected union. Thus, the conventional individualistic employer-employee relationships that would have been set up by the traditional common law of contract and master-servant law was significantly altered in favor for the cartelization of labor. This was done to stave off industrial strife and to assure the continued productivity of American industry at a macro level, even if this meant that some firms would need to eat a loss.
Employees covered by the Act were protected from retailiation for attempting to organize or even for other concerted activities directed to mutual aid and protection (this, importantly includes employees’ discussion of wages, hours, and other conditions of employment — it was this facet of labor law that was implicated in the recent the NLRB settlement with an ambulance provider over a “Facebook firing”).
Here again, notice that the Act up-ends the traditional at-will employment rule. Neither at-will employment nor NLRA-protected employment are required under the Constitution. It is true that a government attempt to forbid employees merely from associating with other employees outside of work would be unconstitutional under the First Amendment. However, the additional protections are not required. Nor is it illicit state action for the government to take adverse employment actions against an employee who is exercising a constitutional right (there’s a NASA case on this which may or may not have the phrase “Merit Board” in its caption). This is the state undertaking acts qua employer, not qua government.