The way the acoustical fanatics do sound isolation is to float the dry wall with drywall isolation rails such as these:
https://www.soundproofcow.com/produc...RoCr34QAvD_BwE
Some go with doubled up drywall glued together to create another natural sound attenuation barrier. Then the wall cavities are filled with either standard fiberglass insulation or cell type acoustically isolating insulation. Any other ingress points such as recessed lights, outlets/wall switches should also be addressed. For recessed lights, the cans are must be IC type if they're going to contact insulation. Some actually build enclosure boxes around them to further isolate any air gaps. The electrical boxes should also be spray foamed where the wiring goes into the box. HVAC registers are also a consideration.
The main reason why many people build out acoustically isolated rooms is not to keep the sound from the A/V room to get out but to block outside noise from getting in.
For me, I opted to keep things relatively simple. I used 5/8" drywall that was glued to all studs and joists. I used fiberglass insulation in all cavities. Flex ducts for the HVAC supply piping to the registers. IC recessed cans. And solid core doors. The rest of the room build was having specific electrical runs wired to the room. I have 3 20A dedicated circuits. Two of them have hard wired balanced power transformers. The last 20A circuit has a component level balanced power transformer. Rest of the money went into acoustical panels.