in 2010 installed 10+ sheets of Quietrock 545 in my listening room. i used it to establish equal side to side solid room boundaries to even out my room bass response. i had a situation where one side was load bearing and the other side was not, which was causing an imbalance in my totally symmetrical room.
i put it around the speaker end walls. even made my window inserts with it.
https://www.quietrock.com/products/quietrock-545
it is 1 and 3/8th thick and very heavy stuff and hard to cut (has a 1/4" layer of aluminum).......will burn through saw blades so your contractor will not like it.
but it works. it's equivalent to 6 sheets of 5/8's sheetrock in sound insulation.
it can be painted like any sheet rock, but i screwed and glued a finished grade maple 3/4" ply over the top of mine. below it my whole room is cocooned with 2 layers of 5/8" sheetrock. as my room is in a barn, a separate building away from my house, which is in the middle of 5 acres in the mountains, and my room is already well insulated for sound, i already had exceptional sound isolation. so i cannot comment on any change on that issue. but it did fix my bass imbalance issue.
if you are already building a room, in the context of material costs it's not that much more compared to other approaches, the labor to install it will be similar. and it will fix problems in one thin layer not otherwise fixed without a much thicker (space-eating) wall.