Before you start...
Minimise or close open windows so you can clearly see messages and instructions displayed during installation.
Essentials
On macOS 13 (Ventura) and above, after installing or upgrading the Cisco Secure client, connecting to VPN displays "Connect capability is unavailable because the VPN service is unavailable." You may also see a warning message in the Connect box saying: "No connection to VPN service. Reattach failed" where normally it would show "Ready to connect". This applies to new installations, manual updates, and forced updates to the Cisco Secure Client - AnyConnect VPN Service.
If you are an Administrator of the Mac, Go into > System Settings > General > Login Items, and make sure the switch against Cisco Secure Client - AnyConnect VPN Service shows as enabled. You can toggle this off and on (for luck) if it is already enabled.
Deep dive
Starting with macOS 13 (Ventura), Apple made changes, including allowing users who have administrative access to their macOS devices, to have more visibility of, and control over, tasks running in the background. Previously, it wasn't possible to view and manage background tasks from the GUI. From Ventura, you can view and change them in System Settings\General\Login Items in the Allow in Background section.
When recent versions of the Cisco Secure Client are installed on devices running macOS 13 (Ventura) and above (including upgrade scenarios), you may be prompted to allow the VPN Service to run in the background. The prompt includes a link to the System Settings and an image to show the setting change you need to make. If you either ignore the prompt or cannot make the change (e.g. because you don't have permission), you won't be able to connect to the VPN.
When the Cisco Secure Client v5 installs or upgrades, you may see one or both of the following prompts:
both require you to make changes in System Settings; the prompts include links.
If you do not allow the socket filter kernel extension, it may continue to show warnings, but the VPN should still work. However, if you don't allow the VPN Service to run in the background, the VPN will not be able to connect.
For University macOS devices managed centrally and where you do not have administrative access, your local IT may need to fix this for you.
Older macOS versions (12 and below) have no way in the GUI to view and manage background tasks, and you may only see the kernel extension prompt.