Ethernet indicator in OSX menu bar
Late to answer but still for those landing here looking for a Ethernet connectivity status icon in menu bar, check this macOS app Ethernet Status - The Missing LAN Status Bar Icon. It shows ethernet interface, IP Address and if interface is active via changing menu bar icon. More here

It does differentiate between WIFI and Wired Ethernet and shows the status for wired ethernet correctly. It also lists the available interfaces and some useful device information.



PS: I am the developer of the app