If you’re using AirPlay you can’t play music and record a video, that’s correct.
Is the music you have in your library music you’ve either purchased from iTunes? If so, you should be able to play that using the method I described, but if your music is only stored locally you won’t be able to do this.
Here are some more detailed instructions in case I wasn’t clear enough.
If you tap the output icon at the bottom of the Now Playing screen, you should get to a screen that looks like this, and then if you tap the bottom panel (not the HomePod in the first panel) you should be able to control your HomePod’s music without using AirPlay.

If your music is only stored locally (i.e. you didn’t purchase it on iTunes and you don’t use iTunes Match) then unfortunately you won’t be able to record snaps/videos whilst playing music.
I don’t know whether AirPlay 2 will fix this, but if this is a deal breaker for you and you’re still within the returns period you might be best to return it now and potentially buy one again if AirPlay 2 does allow recording whilst playing music through AirPlay.