My experience is that most HomePod 'flakiness issues' can be tracked to network problems caused by Apple's "Private Wi-Fi Address" feature being turned ON (the default setting), for the HomePod's WiFi network/SSID, when the HomePod was setup.
The Private Wi-Fi Address setting is defined in iPhone Settings > Wi-Fi > [HomePod WiFi SSID Name] > (ℹ) > Private Wi-Fi Address = [TURN THIS OFF]. Any HomePod setup with Private Wi-Fi Address ON should be factory reset and setup again using an iPhone with "Private Wi-Fi Address = OFF" on the HomePod's network SSID.
NOTE: Turning this 'feature' off will result in a "Privacy Warning" message on the iPhone (in Wi-Fi Settings). This warning can safely be ignored.
TMI: Apple added a "Private Wi-Fi Address" setting to iOS 14. It's a solution-in-search-of-a-problem designed for mobile phone privacy, that sets a flag on each WiFi network an iPhone connects to saying whether or not to use a fake MAC address on that SSID. This value transfers to a HomePod being setup along with other network details. Problem is, the HomePod isn't a mobile device, and it doesn't appear to correctly maintain a table of fake WiFi MAC addresses for each SSID it connects to in order to consistently use the same fake address on each network. The result is that a HomePod setup with Private Wi-Fi Address=ON uses a new Wi-Fi hardware address with every reset/reboot. Whenever this happens, all of the HomePod's peers' apps and WiFi infrastructure devices get confused for a while - particularly on WiFi mesh setups! Simple protocols like AirPlay resolve new addresses quickly and will seem to work OK, thereby causing folks to incorrectly dismiss the notion of a network issue.