No handoff from cellular to wifi

I don't really stream music to my watch, but perhaps there is something in this support article which will help you --> About Bluetooth, Wi-Fi, and cellular on your Apple Watch - Apple Support

It should, mine does. However, I have noticed that leaving wi-fi when I do not have my paired iPhone with me, it can take a little bit of time for the Watch to move to cellular from wi-fi. Like lobsterghost1, I don't stream, and I don't generally leave the house without my iPhone, so it is rarely that cellular goes on my Watch. I did leave last night and went over to my sister-in-law's house. However, because I've been there before, it changed over to her wi-fi, so I'm not sure what would have happened if I received a phone call, since it did not show that cellular was on. I think that is crazy too. I never noticed it because as I said, I rarely do not have my iPhone.