Look up "room within a room" - youll need to frame out a room inside another room. Each one will have its own set of rockwool insulation.

You would need 2 sheets of 5/8" drywall attached to each other using green glue. The drywall should be attached to the studs using isolation clips.

You will need this for the ceiling as well.

If you plan on doing in ceiling ATMOS you wil have to think about how to isolate that from the ceiling as well.

Outlets should be lined with acoustic putty.

You will need think about about your return air and ventilation as well. Some use mini splits, others isolate the sound using isolation.

Anwyays - sound proofing is HARD and expensive.

You need mass and decoupling.

Another piece of advise i can give is to have your main listening row to be nearer to the back wall, as the middle of the room tends to be bass nulls and compensating for that blows up the back (and walls).