It seems that Apple removed this capability in the new OS 16 version, or perhaps it's a bug.
However, you can still play music on the HomePod remotely using Shortcuts. Use the "Control My Home" action, select your HomePod and select what you want it to play (i.e. certain song, album, or playlist). You still won't be able to control it through the Home app even when it's playing, but you could have other shortcuts to pause and resume it if needed. The action can also set the audio volume or use the current volume. You could even do this in an automation to automatically start playing when you leave home.
Another option/workaround... If you have security cameras with two-way audio, you could potentially speak "Hey Siri" commands through those to control the HomePod.