Yes, the list of external speakers is empty on the Mac. And, yes, they are all on the same subnet (via Router DHCP - the AVR is wired, the Mac and iPad are WiFi.) My iPhone is also fine.
OK, then it seems your AVR is only presenting itself as AirTunes (_raop._tcp) target, that's what the first AirPort Expresses did. Only way to tell would be to look at services your Mac sees in Bonjour Browser app.
Looks like - as per the other response - Mac OS Airplay is different from mobile iOS Airplay. :-(
They work the same, but the controls act a little differently.
My AVR not available on the top right of my screen (or when viewing YouTune on Chrome browser), but is available in the iTunes app. :-(
It will never show up in the AirPlay menu. As I said, only video-capable targets will be there. That is, the targets that can serve as wireless displays.
If you see it in iTunes, then the AVR AirPlay works as advertised.
Lately Apple started to distinguish the icons, as you can see in your iTunes screen. AirTunes (was the original name for what AirPort Express did) transmission now has different icon that you can see in iTunes (has waves instead of screen behind the triangle).
I am not sure if the _raop._tcp service is good enough to serve as audio output for macOS. This one may require _airplay._tcp. This would explain why you can use your AVR for playing back music but not as general audio output for macOS.
The bottom line - if you can send music from iTunes to your AVR, then it works as per spec. At least how it was back in 2013 (based on your AVR model).
Over the years, the AirPlay has changed quite a bit and with the introduction of Home Sharing, all 3rd parties are basically ruled out (Home Sharing requires authentication via iTunes Store account / credentials).