Hello and welcome to Apple Support Communities, Peter543!
We understand you're having trouble downloading songs from your iPhone to your Apple Watch SE. We'd be happy to provide information to help you out.
Make sure you've followed all the steps here: Add music to Apple Watch
Add music using your Apple Watch
If you’re an Apple Music subscriber, you can add music using your Apple Watch.
Note: Adding music isn’t available in the Apple Music Voice Plan. For more information, see the Apple Support article About Apple Music Voice.
1. Open the Music app
on your Apple Watch.
2. Tap Library, Listen Now, or Search, then navigate to music you want to add.
3. Tap a playlist or album, tap
, then tap Add to Library.
A message confirms that the item was added.
Note: You can stream music you add to Apple Watch when you have an internet connection. To play music when you’re not connected to the internet, you must first download it.
4. To download the music to Apple Watch, tap
again, then tap Download.
Music is added when Apple Watch is connected to power and Wi-Fi.
If the issue continues, try restarting your devices:
Restart your iPhone
Restart your Apple Watch
Have a great day!