Windows 10 Unable to set ethernet network type (Set to Private)

I urge you to post your diagrams here not in some other site.
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Denis

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The orginial problem PC has switched it's location back to public again too.

Why do my PCs keep doing this every restart?

See:
https://answers.microsoft.com/en-us/...0-44784b9c8193

Which, amongst other things (see the page) says:

The network category (Public/Private) is roamed as part of the "Sync your settings" option (which you can find in the Settings app under the "Accounts" category). If you have multiple Windows devices, it's possible that the setting is being roamed from another device. You might consider disabling setting sync to see if it is the culprit.

Another workaround would be to update the firewall rules to allow remote desktop on Public networks. Alternatively, you can create a scheduled task to use the Set-NetConnectionProfile PowerShell cmdlet to force the network back to "Private".

More:
home networking - Windows 10 keeps switching network location from Private to Public - Super User