Hello Fil017,
Welcome to the Apple Support Communities.
Please be sure to follow these instructions when adding music playlists to your Apple Watch: Listen to music and podcasts on your Apple Watch.
You will also want to make sure that your watch has enough available storage space for the music you are adding. You can check your available storage by opening the Settings app on your watch, then going to General > Usage.
If these are playlists or songs that you also have saved to your iPhone music library, please try to remove the songs from your iPhone then add them back using the Apple Music catalog.
If you continue to notice the same issue, you can unpair and erase your Apple Watch before pairing it and syncing your music again.
Finally, you may want to contact Apple Support directly for more help.
Have a great day!