Not sure I would call this a "bug". By engineering necessity, it has a low-power wifi transmitter. Which means limited bandwidth. Streaming music + separate app streaming video is too much.
And honestly, I don't understand the motivation of streaming music off the watch while at home on your wifi network. Just use the watch to control the stream off your phone. The only case I see where streaming off the watch makes any sense is running/fitness when you don't have your phone with you, and you're not on the same wifi network. But what do I know, somebody will correct me, I'm sure.