You could be right in thinking it is due to a poor mobile data signal, however, I have also seen this problem on here with other users. What seemed to be the problem was their actual headphones. May I ask if you are using AirPods (-/Pro/Max) or if you are using non-Apple headphones? This could be a problem as it is a different sort of Bluetooth connection between AirPods (-/Pro/Max) and Apple Watch, as opposed to non-Apple headphones. To solve the data issue, you could download your playlist(s) to your Apple Watch by going to Music > Library > [Playlist name] > [Three dots] > Download to Apple Watch. Please note that this will transfer best when your Watch and iPhone are connected via Bluetooth and within 10 metres of each other. Should you have any more questions/problems, do not hesitate to reply.