initJoomla.php

<?php
define('_JEXEC', 1);
define('JPATH_BASE', __DIR__);
require_once JPATH_BASE . '/includes/defines.php';
require_once JPATH_BASE . '/includes/framework.php';

// Boot the DI container
$container = \Joomla\CMS\Factory::getContainer();

/*
 * Alias the session service keys to the web session service as that is the primary session backend for this application
 *
 * In addition to aliasing "common" service keys, we also create aliases for the PHP classes to ensure autowiring objects
 * is supported.  This includes aliases for aliased class names, and the keys for aliased class names should be considered
 * deprecated to be removed when the class name alias is removed as well.
 */
$container->alias('session.web', 'session.web.site')
	->alias('session', 'session.web.site')
	->alias('JSession', 'session.web.site')
	->alias(\Joomla\CMS\Session\Session::class, 'session.web.site')
	->alias(\Joomla\Session\Session::class, 'session.web.site')
	->alias(\Joomla\Session\SessionInterface::class, 'session.web.site');

// Instantiate the application.
$app = $container->get(\Joomla\CMS\Application\SiteApplication::class);

// Set the application as global app
\Joomla\CMS\Factory::$application = $app;

var_dump($app);

No, it happens without any changes to Joomla core, when using AdministratorApplication (instead of site) it fails on trying to find 'isis'

I'll take a look later.