Did Apple ever fix the HomePod's "Private Wi-Fi Address" setup bug?
That's exactly what this sounds like - the HomePods all reboot after the update and use a new "Private" WiFi MAC (hardware) address. Everything but AirPlay speaker mode seems to fail for a while afterward until everything in the "Home" learns the new host/ARP tables. [sigh]
Summary of what I'm referring to: Since iOS 14, Apple has set all iOS devices, by default, to use a unique fake Wi-Fi hardware address on each wifi network (supposedly for "privacy"). Unless this "Private Wi-Fi Address" feature is turned OFF for your home WiFi SSID on your iPhone BEFORE you do the initial setup, your HomePod obeys this setting because it copied the network settings from your iPhone. Problem happens when a HomePod reboots and gets new fake hardware address and all the rest of the home network gets a little confused (especially mesh setups). The Fix? Turn off the **** Private Wi-Fi Address "feature" on your Home network for all your iOS devices, then factory reset and setup all your homepods with an iPhone that's using its native WiFi hardware address :-).
Hard to believe Apple hasn't fixed this, it makes their HomePods look super flakey and it's been going on for years now. Google it.
The whole dern "Private Wi-Fi Address" feature is a solution in search of a problem anyways.