How can I clean up (DRY) this verbose jQuery code?
Factor out detailed code into subfunctions

One relatively mechanical thing you could do is transform all of the commented blocks into functions. For a small section, something like this

  // Kill all audio
  $('audio').each(function(){ this.pause(); this.currentTime = 0; });

  // Turn this switch off
  $('.switch01').removeClass('activated');

  // Kill all info cards showing the playback controls
  $('.audio-info-card').addClass('d-none');


becomes

  killAllAudio();
  turnSwitchOff( '.switch01' );
  killAllInfoCards();

  //...

function killAllAudio(){
  $('audio').each(function(){ this.pause(); this.currentTime = 0; });
}

function turnSwitchOff( switch ){
  $(switch).removeClass('activated');
}

// Kill all info cards showing the playback controls
function killAllInfoCards(){
  $('.audio-info-card').addClass('d-none');
}


After this, your top-level algorithm should be much clearer. At the top level it should almost look like pseudocode, except the comments are all calls to subfunctions which do one small named task. 

Factoring out code into subfunctions also helps you see "more code" by abstracting away small details. With shorter functions, you can see more of them on the screen at once.