Not dead yet
My dad recently gave me his first-generation Airport Express, the classic A1084 model released in 2004, because it no longer was recognized by his Sierra-running Macs and Airport Utility networks. RIP, A1084 - Apple stopped supporting you back in 2013 or so...or DID they?
After some well-placed Googling, I found this Apple support doc, and I quote:
“If you have the A1084 or A1088 version, you will need to have.....or be able to borrow for 20 minutes or so.....an older Mac running the Leopard (10.5.x) or Snow Leopard (10.6.x) operating systems, or a PC that has AirPort Utility for Windows installed on the device.”
Just so happens I have a well-aged 2005-era iMac that still capably runs Mac OSX 10.5.7 - the last OS upgrade to the PowerPC iMacs. After about 20 minutes of setting up the old iMac on the home network...it worked! I added that A1084 to my home network using the OS 10.5.7-era Airport Utility app - followed the steps as they still are today in Sierra's Airport Utility app. It will now capably serve as the Airplay base station to my garage workshop stereo.
It lives!