I don't usually render dispersion, but the few times I've done it in the past was by mixing several refraction bsdfs with varying IORs and colors. How do you use white noise for the same effect?

Exactly my thoughts.
I checked the spectral Cycles branch devtalk thread and it seems to be pretty much dead, and this patch looks like the final nail in the coffin.
I hope the work and effort of the community contributed in any way to this, I believe the branch ended in a point where there were too many issues too hard to deal with.

Some more good news is that according to someone who knows more than me presumably (u/Eary in the devtalk forum), I quote:

we can avoid the previous community branch attempt’s complication around E white point and D65 white point CAT adaptation, and we also make the architeture more physically meaningful in a way that the light spectrums can be real known ones with filter, instead of completely arbitrarily uplifted from RGB. [...] This is actually quite elegant

Though they also mention that this implementation has its drawbacks in some specific edge cases and assumptions taken (hardcoded stuff), which would need multiple presets to handle all of them.