How Can the Users Make a “Playlist” of Posts?

What you are looking for is to create a relationship between a Custom Post Type and the Post type.

If your users have editing capability for the CPT, then yes, it’s a good idea to use the CPT’s to hold the information about the Albums (normal posts).

The easiest/fastest solution is to use a plugin.

Posts to Posts is meant exclusively for this (my emphasis):

This plugin allows you to create many-to-many relationships between
posts of any type: post, page, custom etc. A few example use cases:

• manually curated lists of related posts
• post series
• products connected to retailers
• etc.

Additionally, you can create many-to-many
relationships between posts and users. So, you could also implement:

• favorite posts of users
• multiple authors per post
• etc.

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And another one is Advanced Custom Fields. As I’m a regular user, I can illustrate its use for this case.

Create a Field Group with the following configuration:

^{click to enlarge}

That results in this:

The result snapshot have a little trick though. The normal box that ACF generates has a very short height.
To modify the box height, use the following code in your theme’s functions.php file, or a custom plugin which makes this theme independent.

/** 
 * ADJUST THE VALUE OF 'playlists' TO THE CUSTOM POST TYPE SLUG
 * ADJUST THE VALUE OF #acf-album_posts TO MATCH THE FIELD NAME 
 */ 
add_action('admin_head-post.php', 'wpse_73351_admin_head');
add_action('admin_head-post-new.php', 'wpse_73351_admin_head');

function wpse_73351_admin_head()
{
    global $post;
    
    // Not our post_type, do nothing
    if ( 'playlists' != $post->post_type )
        return;     
    ?>
        <style>
            #acf-album_posts select {
                height: 400px !important;
            }
        </style>
    <?php
}

Finally, read the plugin’s documentation to see how to grab the album_posts field value and play that funky music 🙂