In the movie, Midway (2019), there was a scene where the characters portraying Edwin Layton and Chester Nimitz were talking about how Midway Atoll sent out a unencrypted message that the water evaporators in the atoll had apperantly broke. Was this based upon any kind of fact?

Oh, yes, this most assuredly did happen. It's just that it seems to be decontextualised - not having seen the movie, I can't say if either you missed some important setup, or if it just throws it out there expecting the viewer to know what the scene means. More can always be said if anyone would like to expand further on this topic; for the meantime, OP, u/Bacarruda expands on the exploits of Station HYPO, a signals intelligence unit based out of Pearl Harbor.