Win10 system has no Network Profiles (Get-NetConnectionProfile empty)

Question

How to create a new 'Windows Location' setting when there is none set?

For some time now my Win10 Pro system has been running with a perfectly good ethernet stack, but without a 'network location' set, which means some services don't work right (or at all) because Windows is essentially running in 'Public' mode and it disables them.

I have already tried multiple rounds of disabling/deleting drivers, resetting or deleting registry entries and more. I recently came across this post which had some new info. So I now know that:

in an Elevated PowerShell, Get-NetConnectionProfile returns nothing - no entries at all. Using ipconfig in the same window returns the expected info:

PS C:\WINDOWS\system32> ipconfig

Windows IP Configuration
Ethernet adapter Ethernet:
   Connection-specific DNS Suffix  . : ivimey.org
   IPv4 Address. . . . . . . . . . . : 192.168.43.14
   Subnet Mask . . . . . . . . . . . : 255.255.255.0
   Default Gateway . . . . . . . . . : 192.168.43.1

So I tried using Set-NetConnectionProfile:

PS C:\WINDOWS\system32> Set-NetConnectionProfile -InterfaceAlias Ethernet -NetworkCategory Private
Set-NetConnectionProfile : No MSFT_NetConnectionProfile objects found with property 'InterfaceAlias' equal to 'Ethernet'.  Verify the value of the property and retry.
At line:1 char:1
+ Set-NetConnectionProfile -InterfaceAlias Ethernet -NetworkCategory Pr ...
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : ObjectNotFound: (Ethernet:String) [Set-NetConnectionProfile], CimJobException
    + FullyQualifiedErrorId : CmdletizationQuery_NotFound_InterfaceAlias,Set-NetConnectionProfile

I have also tried using -Name rather than -InterfaceAlias with the same result.

Any ideas?