I do not agree that the popular message about increasing labor power in the labor market is beneficial for the capital/employer class. A laborer will more easily dabble with unions or with negotiating harder, etc, when they feel the market is good for them. In fact, that's exactly what we have been seeing, an uptick in union activity. Even if the underlying market strength were not real, it could be a self fulfilling prophecy.
If anything the reverse is true, and a general message that it's hard to find a job is much more benefecial for the capital/employer class, who would then find laborers who are happy to accept anything they can get and have no interest in taking the risk necessary to start or join a union
PS: The last time unions started doing well in the US was also a time when labor was in scarce supply just after WWII. Europe had been destroyed and the USA was the China of the day, but even moreso, in that almost the entire surviving industrial capacity of the world was in the USA. A laborer in the USA, able and willing to operate a factory machine, was thus in terrific, just terrific demand. Unionization happens in good for labor times, to prepare for bad for labor times, not the other way around.