Perfect example of how acoustic treatment can be so confounding: tuning a room with absorption, diffusion, etc., has almost nothing at all to do with stopping transmission of sound in to or out of the room. That’s isolation.
I designed that in to my studio too, within very tight limits. True isolation was not possible; floating floors were not possible, although since the room is a room within a house, sharing no exterior walls, there is a fair degree of ‘accidental’ isolation; but it is not mechanical isolation–vibrations can still be transmitted directly through hard material.
The interior room was built with two layers of 5/8" drywall, solid core doors (HEAVY!, and a pain to install when dealing with custom installations). Crucial is the total elimination of air gaps. Nothing. Not even a 1/4" hole. You will want to caulk every corner, every angle, every seam. All door and window jams must be sealed. There are neoprene-ish, sort of soft, squishy seals you can get, with adhesive backs, that will work.
Windows should be sandwiched between such material; no glass in direct contact with wood, metal, etc. Seal the bottoms of doors, where they contact door frames, etc.
Doors will be tight. Everything will be tight. The room will be pressurized and sealed. If you don’t have HVAC, it’s no problem. Introducing HVAC makes everything exponentially more complicated.
All of the above will go a long way to greatly reducing transmission. It’s not perfect, but it’s good. When I first finished my build, I had a drummer sit and whale away, and I went outside, on the sidewalk, a linear distance of only about 10 feet from where he was playing, and amongst ambient day time noise, he was hard to hear. Across the street, for someone in their house, he was inaudible. Neighbors never said they heard anything.
Sorry for the ramble. I hope it helps a little.
EDIT: I forgot about insulation. I used a non-standard R-value fiberglass insulation; can’t remember the details, and doubled it up. There are other insulations that are not fiberglass that work well for this, but they are very expensive. Thin lead sheeting made for this purpose is also sometimes used.
Oh, I also forgot that behind both layers of drywall is a 1/2" layer of fiberboard. This makes a big difference. It also means your drywall installation will be miserable and a pain, but you’ve got to deal with it. It’s a crap job. The whole thing is miserable and crappy, but when you’re done, you will smile.