Here's what worked for me. Took about a week, but finally we're running fine.
I got two new HomePods on release. Many efforts to install were unsuccessful as HomePods got stuck with message that they were awaiting configuration. At this point, they'd play music, but would not make stereo pair or attach to Apple TV. Both HomePods would not update from version 16.0 factory OS. After reading site, concluded my issue is that I was running the new Home architecture which was released in December then pulled (but only after I'd gotten it installed).
Many troubleshooting moves and many, many resets and 45 min support call later, this is what worked.
Start from Factory reset. Installed from wife's iPhone which is attached to a different Apple ID. Create new "Test" Home and install HomePods there (otherwise would not install as I she was not main home administrator). From here, HomePods were able to successfully update to OS 16.3.1. Confirm all is well and Homepods working out of config state. Do another factory reset. Reinstall with my iPhone on main Home network successful. Delete "test" home from wife's iPhone.
If this didn't work, next move would be to take to a friend's house and have them install on their home network and update to 16.3.1. After that, diconnect from network and do factory reset. Device now in 16.3.1 ready for fresh install at my house. Pretty sure that would have worked too. Key to getting HomePod to work on network with new Home architecture was to update OS to 16.3.1.
Hope that helps.