Hello and thanks for getting back to us. It's never mentioned, can you let us know if the music you have is part of Apple Music subscription, purchased music or music you ripped from CDs?
If you're doing the steps listed in this article, are you making sure that your iPhone and watch are within range, Bluetooth is on and the watch is on its charger? Listen to music and podcasts on your Apple Watch - Apple Support
"How to sync music to your Apple Watch
- Set your Apple Watch on its charger. Make sure that it's charging and that your iPhone is within range of your watch.
- On your iPhone, open the Settings app, then tap Bluetooth. Make sure that Bluetooth is turned on.
- On your iPhone, open the Apple Watch app, then tap the My Watch tab.
- Scroll to Music and tap it.
- Tap Add Music, then find the song or album that you want to sync.
- Tap the Add button
next to the music that you want to sync. If you can't add specific albums or playlists, try downloading them to your iPhone before you sync with your watch"
You've mentioned that there are albums already on the watch, how much storage space do you have available? Keep in mind depending on the total storage you have on the watch determines how much media storage you have available for songs. For example, if you have 32gigs of storage, then you'll have 8gigs available for media storage which includes photos.
After pairing the watch, did you restore any information? How about photos? Do you have any stored? Choose a photo album and manage storage on Apple Watch - Apple Support
"Limit photo storage on Apple Watch
The number of photos stored on your Apple Watch depends on available space. To save space for songs or other content, you can limit the number of photos stored on it."
Make sure that wireless interference isn't causing an issue: Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support If you have any cases, remove the case and see if that works.
If you're still unable to get songs over to your Apple Watch and none of the steps here have been helpful, contact Apple Support.
Best regards.