surely this is a new feature so must be for J5 and require documentation

I have tested this item ✅ successfully on 6ae40ef

Tested successfully in Joomla 4.4.0-dev of 5 May using Wampserver 3.3.1 and PHP 8.2.6

Install any extension.

I installed an extension and it works. The extension is installed.

Can I do an extra check, for example if $this->getDabase() can actually be loaded? Or is not that necessary?

Your installer script needs to use the db aware interface. Then $this->getDatabase() should be filled. If you can test this, that would be perfect.

I have tried something like this in the installer script.php file of mod_readingbar (= test module)

use Joomla\Database\DatabaseAwareInterface;
use Joomla\Database\DatabaseAwareTrait;

class mod_readingbarInstallerScript extends InstallerScript implements DatabaseAwareInterface
{
	use DatabaseAwareTrait;

public function postflight($type, $parent)
{
        // $db = Factory::getDbo(); // works, no error message
        $db = $this->getDatabase(); // works not, see error message below
	echo Text::_('MOD_READINGBAR_INSTALLERSCRIPT_POSTFLIGHT');

Good catch, had to proxy the legacy installer class as well. Can you try again?

I have tested this item ✅ successfully on d58bbc8

I have tried something like this in the installer script.php file of mod_readingbar (= test module)

script.php works now

@toivo can you test this again with your extension? Thanks