Custom Permalink For Custom Post Type – Working Fine But Broken For Pagination

I’m having an issue with pagination not working while trying to get custom post type permalink. I’ve Custom post type ‘songs’ and custom taxonomy ‘singer’ here:

example.com/songs/ // Custom Post Type

example.com/singer/ // Custom Taxonomy

example.com/songs/article // Post Permalink

I want it to look like

example.com/singer/article /// site.com/custom-taxonomy/post

here is my Custom Post Type Code

add_action( 'init', 'your_prefix_register_post_type' );
function your_prefix_register_post_type() {
    $labels = [
        'name'                     => esc_html__( 'Songs', 'your-textdomain' ),
        'singular_name'            => esc_html__( 'Song', 'your-textdomain' ),
        'add_new'                  => esc_html__( 'Add New', 'your-textdomain' ),
        'add_new_item'             => esc_html__( 'Add new song', 'your-textdomain' ),
        'edit_item'                => esc_html__( 'Edit Song', 'your-textdomain' ),
        'new_item'                 => esc_html__( 'New Song', 'your-textdomain' ),
        'view_item'                => esc_html__( 'View Song', 'your-textdomain' ),
        'view_items'               => esc_html__( 'View Songs', 'your-textdomain' ),
        'search_items'             => esc_html__( 'Search Songs', 'your-textdomain' ),
        'not_found'                => esc_html__( 'No songs found', 'your-textdomain' ),
        'not_found_in_trash'       => esc_html__( 'No songs found in Trash', 'your-textdomain' ),
        'parent_item_colon'        => esc_html__( 'Parent Song:', 'your-textdomain' ),
        'all_items'                => esc_html__( 'All Songs', 'your-textdomain' ),
        'archives'                 => esc_html__( 'Song Archives', 'your-textdomain' ),
        'attributes'               => esc_html__( 'Song Attributes', 'your-textdomain' ),
        'insert_into_item'         => esc_html__( 'Insert into song', 'your-textdomain' ),
        'uploaded_to_this_item'    => esc_html__( 'Uploaded to this song', 'your-textdomain' ),
        'featured_image'           => esc_html__( 'Featured image', 'your-textdomain' ),
        'set_featured_image'       => esc_html__( 'Set featured image', 'your-textdomain' ),
        'remove_featured_image'    => esc_html__( 'Remove featured image', 'your-textdomain' ),
        'use_featured_image'       => esc_html__( 'Use as featured image', 'your-textdomain' ),
        'menu_name'                => esc_html__( 'Songs', 'your-textdomain' ),
        'filter_items_list'        => esc_html__( 'Filter songs list', 'your-textdomain' ),
        'filter_by_date'           => esc_html__( '', 'your-textdomain' ),
        'items_list_navigation'    => esc_html__( 'Songs list navigation', 'your-textdomain' ),
        'items_list'               => esc_html__( 'Songs list', 'your-textdomain' ),
        'item_published'           => esc_html__( 'Song published', 'your-textdomain' ),
        'item_published_privately' => esc_html__( 'Song published privately', 'your-textdomain' ),
        'item_reverted_to_draft'   => esc_html__( 'Song reverted to draft', 'your-textdomain' ),
        'item_scheduled'           => esc_html__( 'Song scheduled', 'your-textdomain' ),
        'item_updated'             => esc_html__( 'Song updated', 'your-textdomain' ),
    ];
    $args = [
        'label'               => esc_html__( 'Songs', 'your-textdomain' ),
        'labels'              => $labels,
        'description'         => '',
        'public'              => true,
        'hierarchical'        => false,
        'exclude_from_search' => false,
        'publicly_queryable'  => true,
        'show_ui'             => true,
        'show_in_nav_menus'   => true,
        'show_in_admin_bar'   => true,
        'show_in_rest'        => true,
        'query_var'           => true,
        'can_export'          => true,
        'delete_with_user'    => true,
        'has_archive'         => true,
        'rest_base'           => '',
        'show_in_menu'        => true,
        'menu_position'       => '',
        'menu_icon'           => 'dashicons-format-audio',
        'capability_type'     => 'post',
        'supports'            => ['title', 'editor', 'thumbnail'],
        'taxonomies'          => ['singer', 'rapper', 'category', 'movie', 'album', 'composer', 'lyricist', 'by-year', 'mood', 'file-link', 'post-id', 'yt_id', 'artist'],
        'rewrite'             => array('slug' => 'songs'),
    ];

    register_post_type( 'songs', $args );
}

And Code to rewrite slug for post permalink

function wpa_course_post_link( $post_link, $id = 0 ){
    $post = get_post($id);  
    if ( is_object( $post ) ){
        $terms = wp_get_object_terms( $post->ID, 'singer' );
        if( $terms ){
            return str_replace( '/songs/' , '/' . $terms[0]->slug . '/' , $post_link );
        }
    }
    return $post_link;
}
add_filter( 'post_type_link', 'wpa_course_post_link', 1, 3 );

function custom_rewrite_rules() {
    add_rewrite_rule(
        '^(.*)/(.*)/?$',
        'index.php?post_type=songs&name=$matches[2]',
        'top'
    );
}
add_action( 'init', 'custom_rewrite_rules' );

thank you ahead for any help.