Hi,
I have exactly this issue too. 
Missing field in database: Joomla\CMS\Table\Extension   extension_id.
Our server is working with Plesk. Here are my steps:
- create an empty subdomain 
 
- create an empty database
 
- make sure PHP is 8.1.22
 
- download Quickstart-package (
keynote_quickstart_j4_v2.0.0) for the Keynote-template for Joomla 4 
- unzip the package and upload its contents through FileZilla to the subdomain
 
- start the installer
 
Yet, I get this error message when viewing the 'Issue with Joomla' message in the home-screen of Joomla.