Add the following to your child-theme‘s functions.php :

 

function column_id($columns) {
     $columns['colID'] = __('ID');
     return $columns;
}
add_filter( 'manage_media_columns', 'column_id' );
function column_id_row($columnName, $columnID){
     if($columnName == 'colID'){
          echo $columnID;
     }
}
add_filter( 'manage_media_custom_column', 'column_id_row', 10, 2 );

 

Source: https://halfelf.org/2013/media-library-show-id/