When upgrading to macOS Ventura, Sophos Home will report healthy (green) but the Scan extension will not have full disk access until re-added. This is due to an Apple permissions issue when upgrading to macOS Ventura.
To address this, Sophos Home will prompt users to resolve the missing permissions.

A Welcome to Sophos popup will indicate next steps needed to fully protect macOS Ventura devices

• Click on Let's Start
• Open Security and Privacy using the "Click here" link
• Drag and drop the "Drag This" icon into Full Disk Access
• Click Done

Video steps here:

Note: The above listed problem not happen if you install Sophos Home FOR THE FIRST TIME after upgrading to macOS Ventura. However, existing installations, including re-installations will be affected. This is due to an issue with macOS Ventura not properly allowing Full Disk Access configurations from previous installations, and we have filed a bug with Apple, currently waiting on their input.

There are a few other minor issues with macOS Ventura, noted below.

• After updating to macOS Ventura, you will need to reboot - a second time - for the Sophos Network Extension to be enabled
• Our Transparent Proxy is not working on virtual machines. It is fine on real hardware, but there is no web protection or web control on virtual machines with the current release candidate version of Ventura
• In System Settings, there is a network panel that attempts to allow the user to change the filter state or remove them altogether. The interface is functional but does not affect the Sophos Content Filter or Transparent Proxy - Any changes users make in there will not affect their protection, as they will automatically revert. 

For more info see: Full list of Known Issues