The basic system requirements for Shopware 6 can be found here.
If your version of Shopware is a 6.4, do an update from Version 6.4 to the newest version 6.5 first, before you start the update to version 6.6.
For 6.6 the following versions are required:
PHP 8.2
node-js Version 20
>=MySQL 8 or >=Maria DB 10.11
Git and access to our Git repository
To be able to update to Shopware 6.6, it is necessary to deactivate all extensions. Note also to set the theme to default and deactivate it under extensions.
Only with the extensions deactivated the update from 6.5 to 6.6.
Once on 6.6, the extensions can be updated and then reactivated.
Perform the update as described here in the administration.