Hello @DenisPasternak
My first choice will be also the user added to "Network Configuration Operators" group. Further than that the user "should" be able to change the NIC settings, if there is no other block to it.
I would check the GPOs applying to this user in the path:
User configuration - Administrative Templates Network - Network connections
and in respect to the command line, besides the profile have the rights, it may be needed to select "Open as Administrator" (it may prompt for authentication) to verify the permissions.
Additionally there could be UAC blocking the command as Powershell or CMD are not "GUI" sensible and wouldn't always prompt for UAC validation. Try the next:
In the registry of the machine:
path: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Policies\System\
Key: ConsentPromptBehaviorUser
Set the value to: 3
Reboot and test again.
Hope this works for you!
Best regards,