This is a little interesting, I used strava on my apple watch for my commute. I also play music from my phone on one wireless earbud. I can do my 40 mile RT commute (2.5 hours) along with standard watch use during the day, and still have ~60% battery left by the time I get home. That said, I did notice that if I played music from the watch or used my podcast player, it drained my watch battery VERY quickly. So based on experience, the issue might not be with strava, but another watch app you are using. Try playing music from the phone and not the watch. The watch should still let you control the phone and music playing, but it’s not using the watch music app itself.