There's a sneaky menu bar background noise app already built into MacOS. You can add "Hearing" to the menu bar (or control center) from settings, and then use that to enable "Background Sounds"
It's probably easier to get buy-in from stakeholders if what you want to add is hidden behind menu options (reduced risk).
Only affects the background noise feature, doesn't affect any other sound, music or video. I have no idea what causes it.
Is "Dark noise" the equivalent of "Brown noise"?
Note: Generally "dark" (as opposed to "bright") means emphasis on the lower frequencies, which is a good description for brown noise, but they aren't formally the same. Formally, brown noise refers to a power distribution that drops ~6 dB per octave, and I have no idea how strictly apple's "dark noise" matches the technical specifications of that.