Door sound deadening

you're in luck, i'm an acoustical engineer and i spend a lot of time helping spaces be quieter by increasing transmission loss of doors, windows, walls, etc.

the primary source of noise transfer through a door is under it. if it's not water-tight, it's letting a lot of sound through the gaps.

you want to add seals around the door and especially the bottom gap. weatherstripping foam can be used for the top and sides.

for the bottom, you can start with a draft-blocker bottom seal which is just two pieces of foam pipe insulation in a fabric sleeve so the foam is on both sides of the door bottom.

the hollow door itself can be addressed after you've sealed the top, bottom, and sides. from there, transmission loss is increased by adding mass that is decoupled from the door (decoupled with foams or fabrics). you'll need 100% coverage that meets up with the door seals.

adding sound absorption in the hallway will help reduce source noise levels. there are many ways to do this. my favorite is to get some fiberglass ceiling tiles and put them behind painted canvas. it's cheap and very effective.

A roll of weather stripping foam should be $3 or so and you will need two rolls. Thickness should depend on how much of a gap you have. You want it to compress but not impede on operation of the door

You could replace the foam in the draft blocker with PVC that is covered in felt and stuffed with some sound absorption

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