you can fit dense fire doors, which are good at muffling noise, but not more than two, because folding arrangements of doors are difficult to seal tightly. You can have then meeting with an overlapping rebate, and you can fit the furry pile smoke strip (which further muffles noise and draughts) on the meeting edge, and on the frames so it touches the door all round (except underneath). The door frame, or lining, should be tightly fitted to the hole in the wall, and sealed all round with pink (fire grade) expanding foam. Fire doors have the added advantage that they are quite heavy, so they give an impression of being substantial and good quality (though the filling is usually only chipboard). You can get paint grade or veneer, flat or panelled. They start at about £80 per door and go up to whatever you like. Avoid the ones with a tawdry imitation woodgrain embossing.
Any competent carpenter will know how to do this, because what I am describing is a standard fire door installation, but it is also good for noise. There are specialist sound-reducing doors available, and specialist fitters, if you are willing to spend considerably more.
This will be OK in an ordinary brick or block wall, which is about 125mm thick including plaster. In the unlikely event that your door is about 250mm thick, you could, if you wanted, have a pair of doors opening into each of the communicating doors, with an air-gap between. This is sometimes done in communication hotel rooms as it reduces sound more.
You can get self-closers if you think people will leave them open, but this is a bit ungainly with pairs of doors.