Is the "Private Wifi Address" setting synced between devices across iCloud?

As a nerd, I want all the devices on my home network to always use their hardware MAC address when connected to my WiFi. Partially because my Eero system maps devices to their MAC addresses and I always want to know which device is which, and not sometimes showing up as "Private Device"

I keep the Private Address option to off on my iOS/iPadOS/WatchOS devices, but it keeps "turning itself" back on.

My questions are:

Is Private Address a local device setting that I could have on or off on each device?

Or, is it synced to iCloud as a network setting for all devices, like the password?

The behavior I'm seeing seems to be that it's synced, or at the least the DEFAULT setting is Fixed and it's turning itself back to default each time you update the device.

It's really annoying me and would love to understand the behavior