in the apple music app, look at the bottom middle under the airplay icon, if you see only the name of your HomePod, then the music app is functioning only as a remote for the HomePod. so as stated, everything will stream from apple directly to the HomePod. You'll also see this on the Lock Screen controls, the name of the device will appear above the song title.
If you see "iPhone -> Living Room" then it's playing on your phone, and streaming via airplay to to the HomePod in the living room.
and if you just see "bedroom + living room" then it's playing on one of those 2 devices, and airplaying to the other.
on either of the airplay selection screens (from control center, or in the music app) there is a "control other speakers and TVs" option at the bottom, that will let you select which device you're actually playing on.
This also applies to appleTVs.
If you ask siri for something on the HomePod, it will play directly on the homepod.