OK, so this is my original thread and hopefully it'll get fixed by Apple now that a few users reporting the same problem.
As a few people have noted, the problem is to do with using your HomePod as the default audio output for an Apple TV. I believe the Apple TV goes into a deep sleep mode after a few hours of not being used, and doesn't get awoken properly by the HomePod that wants to coordinate the music that's playing with the onscreen graphics of the Apple TV.
The workaround solution to my case is to manually restart the Apple TV via the settings.
Yesterday I gave a really nice Apple helpline man all my logs for both my Apple TV 4K and my Apple HomePod, plus I wrote out a few timeline logs to help with reproducing the problem and also implementing the workaround solution. Here's one of them:
Case #01 - Friday, 8th October.
Apple TV hasn't been used overnight.
07:38:30 User ➡ HomePod: "Hey siri, play chill house."
07:38:35 HomePod ➡ User: "Chill house now playing"
07:39:05 HomePod ➡ User: "Sorry, there was a problem with Apple Music"
07:40:40 User ➡ HomePod: "Hey siri, play chill house."
07:41:15 HomePod ➡ User: "Sorry, there was a problem with Apple Music"
07:42:?? User turns on Apple TV 4K via the remote
07:42:40 User ➡ HomePod: "Hey siri, play chill house."
07:43:08 HomePod ➡ User: "Sorry, there was a problem with Apple Music"
07:43:30 User restarts Apple TV 4K (Settings ➡ System ➡ Restart)
07:44:50 User ➡ HomePod: "Hey siri, play chill house."
07:44:55 HomePod begins to play music