After searching for a while through the various discussions, I realized, that the current editions of Windows 10 (1803) are lacking this functionality.
I eventually came across a small freeware utility, which does exactly what I was looking for. It has been around for a few years and is still compatible with Windows 10:
VPN Connection Indicator
VPN Connection Indicator displays a VPN indication icon in the
traybar. Whenever there is a VPN connection active, the icon changes
to the connected state.
This utility is a standalone executable that is installed (by default)
in the current users startup menu. This means that every time you log
on to your computer this utility is started automatically and is
visible in the traybar.
You can right-click on the icon and select which VPN connection to
monitor (or any if you just want to know of any VPN connection).
The author's website is: http://www.weseman.net/vpnconnectionindicator/
In case this becomes unavailable, it should still be downloadable from MajorGeeks at https://www.majorgeeks.com/files/details/vpn_connection_indicator.html