Self instantiating class with static methods implementing from WordPress plugin

I'm developing a WordPress plugin. I'm new to PHP OOP, BTW adopted an advanced method for implementing things by following one of the advanced WordPress plugin. And now stuck somewhere. I can get back to procedural PHP, but things will be untouched if I get back from this far.

I understood what I did, but may be something I'm missing, and that's why I'm seeking your very intuitive look to my code, what am I doing wrong.

Main class with self instantiation

<?php
if ( ! class_exists( 'Xyz' ) ) :

final class Xyz {

    /**
     * Xyz version.
     * @var string
     */
    public $version = '1.0.0';

    /**
     * @var Xyz The single instance of the class
     */
    protected static $_instance = null;

    /**
     * Main Xyz Instance.
     *
     * Ensures only one instance of Xyz is loaded or can be loaded.
     * 
     * @static
     * @see XYZ()
     * @return Xyz - Main instance
     */
    public static function instance() {
        if ( is_null( self::$_instance ) ) {
            self::$_instance = new self();
        }
        return self::$_instance;
    }

    public function __construct() {
        $this->define_constants();
        $this->xyz_includes();
        $this->init();
    }

    /**
     * Define constant if not yet set.
     *
     * @param string        $name
     * @param string|bool   $value
     */
    private function xyz_define( $name, $value ) {
        if ( ! defined( $name ) ) {
            define( $name, $value );
        }
    }

    /**
     * Define necessary constants
     */
    private function define_constants() {
        $this->xyz_define( 'XYZ_PLUGIN_FILE', __FILE__ );
        $this->xyz_define( 'XYZ_PLUGIN_BASENAME', plugin_basename( __FILE__ ) );
    }

    /**
     * Include additional files
     */
    public function xyz_includes() {
        /** Classes **/
        include_once( 'includes/class-xyz-install.php' );

        /** Core Functions **/
        include_once( 'includes/xyz-core-functions.php' );

        //...and so on...
    }

    public function init() {
        register_activation_hook( __FILE__, array('XYZ_Install', 'install') );
        add_action( 'init', array( $this, 'xyz_load_textdomain' ), 1 );
    }

    /**
     * Make the plugin translation-ready.
     */
    public function xyz_load_textdomain() {

        load_plugin_textdomain(
            'xyz',
            false,
            dirname( plugin_basename( __FILE__ ) ) .'/languages/'
        );
    }
}

endif;

/**
 * Returns the main instance of Xyz to prevent the need to use globals.
 * @return XYZ
 */
function XYZ() {
    return Xyz::instance();
}

includes/class-xyz-install.php

<?php
class XYZ_Install {

    public static function init() {
        add_filter( 'plugin_action_links_'. XYZ_PLUGIN_BASENAME, array( __CLASS__, 'plugin_settings_link' ) );
    }

    public static function plugin_settings_link( $links ) {
      //$links = existing links + made up link
      return $links;
    }

    public function install() {
        delete_option( 'xyz_version' );
        add_option( 'xyz_version', XYZ()->version );

        xyz_register_cpt_xyz();
        flush_rewrite_rules( false );
    }

}

XYZ_Install::init();

When I started developing the plugin the self instantiation was working fine, and I's getting all the values from its properties (var).

I enabled procedural coding for register_activation_hook() and other includes. But when I then implemented them using the final class, they stopped working.

1. The includes are not working. If I put them a procedural function something(), and simply call it somewhere something(); the includes are working fine.
2. I'm not sure whether my register_activation_hook() inside the class is correct or not.

I'd love to learn PHP OOP from my mistakes. Any assistance would be greatly appreciated.

Edit 20180107

Fixed a typo NS_Install with XYZ_Install.