WordPress custom post type taxonomy (book/taxonomy-name/page/2)

functions.php

<?php

add_action( 'init', 'codex_book_init' );

function codex_book_init() {
	$labels = array(
		'name'               => _x( 'Books', 'post type general name', 'your-plugin-textdomain' ),
		'singular_name'      => _x( 'Book', 'post type singular name', 'your-plugin-textdomain' ),
		'menu_name'          => _x( 'Books', 'admin menu', 'your-plugin-textdomain' ),
		'name_admin_bar'     => _x( 'Book', 'add new on admin bar', 'your-plugin-textdomain' ),
		'add_new'            => _x( 'Add New', 'book', 'your-plugin-textdomain' ),
		'add_new_item'       => __( 'Add New Book', 'your-plugin-textdomain' ),
		'new_item'           => __( 'New Book', 'your-plugin-textdomain' ),
		'edit_item'          => __( 'Edit Book', 'your-plugin-textdomain' ),
		'view_item'          => __( 'View Book', 'your-plugin-textdomain' ),
		'all_items'          => __( 'All Books', 'your-plugin-textdomain' ),
		'search_items'       => __( 'Search Books', 'your-plugin-textdomain' ),
		'parent_item_colon'  => __( 'Parent Books:', 'your-plugin-textdomain' ),
		'not_found'          => __( 'No books found.', 'your-plugin-textdomain' ),
		'not_found_in_trash' => __( 'No books found in Trash.', 'your-plugin-textdomain' )
	);

	$args = array(
		'labels'             => $labels,
        'description'        => __( 'Description.', 'your-plugin-textdomain' ),
		'public'             => true,
		'publicly_queryable' => true,
		'show_ui'            => true,
		'show_in_menu'       => true,
		'query_var'          => true,
		'rewrite'            => array( 'slug' => 'book/%genre%' ),
		'capability_type'    => 'post',
		'has_archive'        => true,
		'hierarchical'       => false,
		'menu_position'      => null,
		'supports'           => array( 'title', 'editor', 'author', 'thumbnail', 'excerpt', 'comments' )
	);

	register_post_type( 'book', $args );

	register_taxonomy(
		'genre',
		'book',
		array(
			'label' => __( 'Genre' ),
			'rewrite' => array( 'slug' => 'genre' ),
			'hierarchical' => true,
		)
	);
}

add_filter( 'post_type_link', function ( $post_link, $post ) {
    $terms = wp_get_object_terms( $post->ID, 'genre' );
    if ( $terms ) {
        return str_replace( '%genre%' , $terms[0]->slug , $post_link );
    } else {
        return str_replace( '%genre%/' , '' , $post_link );
    }
    
    return $post_link;
}, 1, 2 );

add_filter('init', function() {
    add_rewrite_rule( 
        '^book/([^/]*)/([^/]*)/(\d*)?',
        'index.php?genre=$matches[1]&p=$matches[2]&paged=$matches[3]',
        'top' 
     ); 
});