Something somewhere does seem terribly goofy. I have solid WiFi and Internet in the house. Two stereo pair HomePod setups; one in the bedroom, one in the kitchen.
After I removed the HomePods, adding them back was a nightmare. I kept getting Setup Failed -71147. And then retrying, until it’d work. To work through all four HomePods took about twenty tries.
After getting the HomePods all set up, it does seem that getting the Home app to allow personal requests takes an hour or two for everything to settle in. There’s no indication of what is happening, and worse, there’s an error showing “Voice Recognition is not available on this HomePod” but simply waiting an hour fixed it.