The easiest way probably would be to export a sweep with and without dithering enabled in Audacity’s settings, and then compare the files in a hex editor
Audacity will apply dither by default, unless you have just imported a file and then exported it right away. In this case Audacity is smart now (thanks, Paul) and won’t apply the dithering.
This is a “clean” 3.4.2, so the default Dither On should be there, but I can check.
I generated Silence and then exported it as a WAV file. I can’t find any additional noise, even after much amplifying.
But to the original idea. There is a version of noise (shaped??) that’s all high pitch and low pitch with nothing in the middle. It does its job and it’s harder to hear.
Is there a version that “knows” what the show volume is? That would seem to be insanely complicated, but may make the dither insertion less obvious.