The problem here is missing what you shoot at.

Most discussions about over penetration are really about missing the target.

A load of birdshot (#7 1/2 or 8) will certainly penetrate a sheet or two of drywall at in house distances.

It will also inflict a truly grievous wound without penetrating a man’s torso, certainly not with enough remaining energy to do much damage to a sheet of drywall let alone anything beyond the drywall.

As in most sd situations, hitting what you’re shooting at is important.