Hi there AppletheGOAT,
You'll want to be sure you're following the steps below to add your music to your Apple Watch:
How to sync music to your Apple Watch
1. Set your Apple Watch on its charger. Make sure that it's charging and that your iPhone is within range of your watch.
2. On your iPhone, open the Settings app, then tap Bluetooth. Make sure that Bluetooth is turned on.
3. On your iPhone, open the Apple Watch app, then tap the My Watch tab.
4. Scroll to Music and tap it.
5. Tap Add Music, then find the song or album that you want to sync.
6. 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'll find this information here: Listen to music and podcasts on your Apple Watch - Apple Support
If you're following those steps and it's still not working, we'd suggest making sure your iPhone and Apple Watch are both running the latest software versions. For your iPhone, it's iOS 16.2 and for your Apple Watch, it's watchOS 9.2. You can check the currently installed software versions on both devices by going to Settings > General > About. Learn more about updating your iPhone and Apple Watch from the links below:
Update your iPhone or iPad - Apple Support
Update your Apple Watch - Apple Support
If the issue persists beyond that, you may want to try syncing your music to your iPhone again, then attempt to add it to your watch again. This link provides instructions if needed: Sync your iPhone, iPad, or iPod using your computer - Apple Support
For more help, reaching out to Apple Support directly is the next best steps. They're better-suited to take a closer look at the issue and provide some additional guidance. This link will help you get started: Contact - Official Apple Support
Take care!