How to search titles/artist/album within a playlist, and only lists the results that match?

I unhook the wp_underscore_playlist_templates() function and create
my own version prefix_wp_underscore_playlist_templates()

You should first get back to or restore the default playlist template. (i.e. Hook back to wp_underscore_playlist_templates().)

Add then add this somewhere in the theme’s main functions.php file:

add_action( 'wp_playlist_scripts', function(){
    ?>
<script>
jQuery( function( $ ){
    // Add the search box.
    $( '.wp-playlist' ).prepend(
        '<p class="wp-playlist-custom-search alignright">' +
            '<input class="search-playlist" placeholder="Search" />' +
        '</p>' +
        '<div style="clear: both;"></div>'
    );

    // Performs the search.
    $( '.search-playlist', '.wp-playlist' ).on( 'keyup', function( e ){
        var $playlist = $( this ).closest( '.wp-playlist' ),
            query = this.value;

        if ( ! query ) {
            $( '.wp-playlist-item', $playlist ).show();
            return;
        } else if ( e.key.length > 1 ) {
            return;
        }

        $( '.wp-playlist-item-title', $playlist ).each( function(){
            var re = new RegExp( '(' + query + ')', 'ig' ),
                title = $( this ).text();

            if ( re.test( title ) ) {
                $( this ).closest( '.wp-playlist-item' ).show();
            } else {
                $( this ).closest( '.wp-playlist-item' ).hide();
            }
        } );
    } );
} );
</script>
    <?php
} );

You’d get a search box that looks something like:

And this, upon searching: