Hi mike_bp,
A good first step in troubleshooting any device concern is to restart the unit. If HomePod or HomePod mini isn't responding describes that process as:
"Restart HomePod or HomePod mini
- Open the Home app on your iPhone, iPad, or Mac.
- Tap or click HomePod, then tap or click the Settings button.
- If you have two HomePod speakers set up as a stereo pair, select Restart HomePod. If your HomePod speaker is not set up as a stereo pair, select Reset HomePod, then select Restart HomePod.
If you don't see an option to restart your HomePod, unplug it from power, then plug it back in and try again.
If HomePod still doesn't respond, reset it."
If unsuccessful, further isolation would prove helpful. You mentioned a specific genre of music, but are other genres impacted? If you start the song on your iPhone and use AirPlay to stream to the HomePod, are these issues present? Do they occur at all on the iPhone?
The results of these steps would be valuable to continue investigating with Apple Support directly.
Regards.