www.homedepot.com/p/…/319880476

This is the kind of thing I would suggest, it’s designed to be soundproofing, fire retardant home insulation. This is literally the exact thing you would put in-between your joists before drywall if you were trying to insulate an interior wall for sound.

There’s a product called green fiber that is a blown-in cellulose insulation that’s been treated with fire retardant you could use if the walls have already been drywalled, I’ve used that in all of the interior walls of my home when I was remodeling to try and deaden sound and have added privacy throughout the home. My basement, which I turned into a mother-in-law apartment, is so private I can’t hear my basement neighbor when they have their video games blasting through a surround sound stereo set with a subwoofer. I can feel the floor shake but, unless I am standing right next to a vent, I can’t hear anything.