I found furniture moving blankets work pretty well.
You don’t have to soundproof the whole room. I published a Kitchen Table Sound Studio.
https://forum.audacityteam.org/t/too-compressed-rejection/52825/22
I made a portable sound studio I throw in the back of my truck for remote shoots. This has wooden stands and clamps, but I can construct a sound shoot anywhere in about a half-hour.
This woman constructed a studio out of plumbing pipes.
Pipes and moving blankets have the advantage that you can get the materials from many well-equipped home centers.
Packing and shipping foam seem to be ideal candidates for sound proofing, but they’re not. The key word is “Heavy.” Sound has to move the panels or blankets. Shipping foam’s job is to take up space and be light.
As above, whatever you choose is going to work best if it’s separated from the wall by at least an inch or two.
Don’t forget the floor. The floor and ceiling represent two hard opposing surfaces. Note in the first illustration, there’s a folded up moving blanket on the floor.
Koz