In a very amateurish way, have ordered a roll of weather strips to run around either the door or doorframe. Should arrive next week.
The current door is very "gappy" (5 mm on three sides!) Between when it's open and closed, the difference is 5 dB.
Hoping to seal it, and see how it sounds outside the room, too.
For the bottom (something similar to the links, not necessarily the exact item) -
An automatic drop-down seal for doors consists of an external aluminum profile (1) (of variable dimensions depending on the model and on the door system in which it will be installed) and of a second inner aluminum profile (2) that is pushed downwards by rigid trust-roads in plastic material...
For the sides (not sure if it will work with 5mm, may need something similar but thicker) -
Glasswool, Rockwool, Foam, Acoustical Foam, Genset Accessories, HVAC Accessories, Hinges, Locks, Sealing Tape
I have something similar to these on my door.