what service are you using? Apple Music or something else.
how are you playing music....
on the phone, and then air playing to the HomePod?
or
directly on the HomePod? (only available w/Apple Music)
which Siri are you asking to play music? phone or HomePod?
in the now playing tile on your phone's Lock Screen if it says "iPhone --> homepod name" then it's airplaying
if it says "HomePod name" then it's playing on the speaker.
if you're playing music your phone, it's highly possible that music is indeed playing on the phone, but failing in the airplay step that makes the music come out of the HomePod.
if you're using Apple Music, try asking Siri on the HomePod to play something, or use hand off, get something playing on your phone, and hold the phone over the homepod (you need a recent-ish phone to do this, think it's an 11 or newer)
for Apple Music, hand off transfers the music to the player in the homepod
for other services, hand off will start airplay from your phone,
for any other services, the music plays on your phone, and the airplays to the HomePod.
for airplay issues, the first step is rebooting your router.
If you're using airplay, and your HomePod is at the far end of your house from your wifi, you may have issues. Airplay needs a fairly stable connection to work, since the stream is basically live, it can't buffer too much, so is affected by drop outs. Playing music directly on the HomePod can sort this out, since the file already exists, the hompod can buffer the entire song, and possibly the next.
if you're using Apple Music.
open the airplay menu, and at the bottom of the screen hit "control other speakers and TVs". You'll see the HomePod listed there, if you select that, the music app is now a remote for the player in the HomePod.