Yesterday, 16 December 2022, Apple has updated the Private Relay page
https://support.apple.com/en-us/HT212614
Private Relay is no longer listed as “Beta”.
About VPNs:
“If your system settings prevent Private Relay from working
In System Settings on your Mac, you might see an alert that says "Some of your system settings prevent Private Relay from working." If you do, a third-party app — such as a VPN or internet filtering software — might have installed settings or extensions that are incompatible with Private Relay. For example, the third-party app might have installed a kernel extension or applied custom packet filter rules.
If you want to use Private Relay on your Mac, turn off or uninstall the third-party app.”
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