Sometime in 2019, Apple quietly changed how the HomePod is counted by the Apple Music service as a streaming device, resulting in a slightly more restrictive device for the end-user.
The net effect of the change, as pointed out by a Redditor, is that if you have a single-user Apple Music subscription, if you start a stream on your iPad or iPhone, it stops what's playing on your HomePod, and vice versa. This appears to be how Apple intended it all along, as none of the marketing materials have ever suggested otherwise, nor have there been exceptions carved out for the HomePod in Apple's terms of service for Apple Music.
The $9.99 per month Apple Music subscription allows for one stream. The $14.99 per month membership doesn't have this restriction, and allows for six different streams across all of the user's devices either on that Apple ID, or others linked by Family Sharing.
One stream being played by multiple HomePods attached to an account still counts as one device. Local playback of iTunes media stored on a hard drive not acquired from Apple Music of original files not downloaded as a match from Apple's servers does not count as a stream.
Multiple users on Reddit confirmed that they had been told the same thing. Apple Support representatives were telling users that called in that the previous behavior was a bug, and the current HomePod behavior is how the device was intended all along.
It isn't clear when the change took place. AppleInsider can confirm that the previous behavior manifested at least through New Year's Day. There hasn't been an official OS update in 2019 as of yet, so the change must have been made server-side, and it appears to be rolling out gradually.