Unable to load stylesheets and scripts to plugin settings page

The way to go was to use wp_enqueue_style() and wp_enqueue_script functions when admin_enqueue_scripts hooks.

To register styles and scripts with wp_register_style and wp_register_script respectively is optional, but has some good advantages as nicely explained here.

Here’s the working script:

<?php
/*
Plugin Name: Awesome Slide Show
*/



// admin_init
// ************************************************************************************************
    function wp_ss_plugin_admin_init_cb() {
        // Register CSS
        wp_register_style(
            'wp_ss_plugin_style', plugin_dir_url( __FILE__ ) . '/settings/style.css'
        );

        // Register JS
        wp_register_script(
            'wp_ss_plugin_script', plugin_dir_url( __FILE__ ) . '/settings/script.js',
            'jquery' //jQuery dependency
        );
    }
    add_action('admin_init', 'wp_ss_plugin_admin_init_cb');



// admin_enqueue_scripts
// ************************************************************************************************
    function wp_ss_plugin_admin_enqueue_scripts_cb() {
        //Enqueue CSS
        wp_enqueue_style('wp_ss_plugin_style');

        //Enqueue JS
        wp_enqueue_script('wp_ss_plugin_script');
    }
    add_action('admin_enqueue_scripts', 'wp_ss_plugin_admin_enqueue_scripts_cb');



// admin_menu
// ************************************************************************************************
    function wp_ss_plugin_admin_menu_cb() {
        add_menu_page("Slide Show", "Slide Slow", "manage_options", "wp-ss-plugin", 
            function () {
                require "settings/index.php";
            }
        );
    }
    add_action('admin_menu', 'wp_ss_plugin_admin_menu_cb');



?>

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One more issue I faced was that even after scripts and styles were working, jQuery was not. And that was solved after adding jQuery as a dependency to my script using the third parameter of wp_register_script.