How to make my custom widget appear within WordPress widgets? Plugin development

Question

This is my first WordPress plugin ever, so i'm a little noob. But why is my widget not showing within all the other widgets in my WP-Admin interface? It should be visible when i activate the plugin. But it's not. Any help appreciated!

includes/class-level_system-widgets.php

class Level_system_Widgets extends WP_Widget {

    public function __construct(){
        $widget_ops = array( 
            'classname' => 'my_widget',
            'description' => 'My Widget is awesome',
        );
        parent::__construct( 'my_widget', 'My Widget', $widget_ops );
    }

    public function widget( $args, $instance ) {
        // outputs the content of the widget
    }   

    public function form( $instance ) {
        // outputs the options form on admin
    }

    public function update( $new_instance, $old_instance ) {
        // processes widget options to be saved
    }

    public function init() {
        add_action( 'widgets_init', function(){
            register_widget( 'My_Widget' );
        }); 
    }
}

level_system.php

function activate_level_system() {
    require_once plugin_dir_path( __FILE__ ) . 'includes/class-level_system-widgets.php';
    Level_system_Widgets::init();
}

Answer 1

Updated my answer based on your comments. First of all;

Please read how to create a plugin: https://codex.wordpress.org/Writing_a_Plugin

Secondly, create a folder and your file in the wp-content/plugins directory. Add this sample plugin code below.

After that please activate the plugin from Dashboard.

old answer

When you register widget as a plugin you need to use add_action after your class. widgets init loads before your class.

add_action('widgets_init', create_function('', 'return register_widget("Level_system_Widgets");'));

Add this code after your class (Code Updated with sample WordPress Widgets API code);

New Answer

<?php
/*
Plugin Name: Did you try this widget?
Plugin URI: http://www.serkanalgur.com.tr/
Description: Did you try this widget?
Version: 1
Author: Serkan Algur
Author URI: http://www.serkanalgur.com.tr
License: GPL2
*/

class Level_system_Widgets extends WP_Widget {

    public function __construct() {
        $widget_ops = array(
            'classname'   => 'level_system_widget',
            'description' => 'Level System Widget',
        );
        parent::__construct( 'level_system_widget', 'Level System Widget', $widget_ops );
    }

    public function widget( $args, $instance ) {
        echo $args['before_widget'];
        if ( ! empty( $instance['title'] ) ) {
            echo $args['before_title'] . apply_filters( 'widget_title', $instance['title'] ) . $args['after_title'];
        }
        echo esc_html__( 'Hello, World!', 'text_domain' );
        echo $args['after_widget'];
    }

    public function form( $instance ) {
        $title = ! empty( $instance['title'] ) ? $instance['title'] : esc_html__( 'New title', 'text_domain' );
        ?>
    <p>
    <label for="<?php echo esc_attr( $this->get_field_id( 'title' ) ); ?>"><?php esc_attr_e( 'Title:', 'text_domain' ); ?></label> 
    <input class="widefat" id="<?php echo esc_attr( $this->get_field_id( 'title' ) ); ?>" name="<?php echo esc_attr( $this->get_field_name( 'title' ) ); ?>" type="text" value="<?php echo esc_attr( $title ); ?>">
    </p>
        <?php
    }

    public function update( $new_instance, $old_instance ) {
        $instance          = array();
        $instance['title'] = ( ! empty( $new_instance['title'] ) ) ? sanitize_text_field( $new_instance['title'] ) : '';

        return $instance;
    }

}

function register_widgets() {
    return register_widget( 'Level_system_Widgets' );
}
add_action( 'widgets_init', 'register_widgets' );

This code works. Tested with latest WordPress version (v5.8.1 as 26.10.2021)