Hello,
I once made a test with Joomla 4.3.4 on Joomla 4.4.0 Alpha 4.
A small text with video about it can be found here (but in German):
https://forum.joomla.de/thread/19048-ready-for-joomla-5-liste-von-templates-frameworks-erweiterungen-und-plugins-die/?postID=138567#post138567

After the update there are a lot of error messages in the frontend, I guess that is related to this:

Deprecated: Creation of dynamic property Astroid\Document::$modules is deprecated in /html/cms/libraries/astroid/framework/library/astroid/Document.php on line 582

The error also seems to be related to that:
ERROR 0 - Database not set in Joomla\Module\RelatedItems\Site\Helper\RelatedItemsHelper in /html/cms/libraries/vendor/joomla/database/src/DatabaseAwareTrait.php:43

The total error messages look like this:

WBR,
deltapapa