I have a message saying, "Your system settings are incompatible with Private Relay," and the help sent me here. However, it doesn't tell me what system settings to change. What system settings are incompatible?

About iCloud Private Relay

Note: iCloud Private Relay is not available in all countries or regions and is currently in beta in iOS 15, iPadOS 15, and macOS Monterey.

How are the iPhone and iPad connecting to the Internet ?

How is the computer connecting to the Internet ?

If the computer connecting from behind a VPN which could be use a Server that is outside of your Region.

Try this external link to Test what the service is on the computer and if it matches your Actual Location and Region.

https://www.iplocation.net

My region is coming up correctly. I did turn off the CISCO any connect that we use every now and then to log into a university site. I turned off Private relay and turned it back on and it appears to be working now... at least it is showing green. So it may have been my issue being we used any connect last night -- but we logged out of any connect last night... but may still have caused an issue with private relay

It works on my Iphone and iPad but not on my MAC. So not Sure it is a region issue as the error states it is a system issue

Good procedure you used to pinpoint the possible root cause of this issue.