I did not see an Update option for my AirPort Express.
This would indicate one of two things:
1) The AirPort Express already has the most up to date firmware
2) The Update option did not show since you were having other difficulties. In that case...and if the AirPort has not been updated....the amber light will likely start blinking in the next few days.
Quite frankly I struggled to make sense of the apple link info
The Apple document is unfortunately not easy for most users to understand and use....one of the reasons I tried to simplify things for you.
Turning off airport at the iMac and only choosing Ethernet somehow seemed to do the trick.
If the iMac is connected using Ethernet, then the WiFi at the iMac should not be turned on. Conversely, if the iMac is connected using WiFi, then the Ethernet cable should be disconnected at the iMac. Reason.....having both WiFi and Ethernet turned "on" at the same time on a Mac can sometimes create connection problems that are difficult to identify and solve.