Home Sharing won't play through Bluetooth 2.0 with temporary fix until they fix the bug...
Home Sharing won't play through bluetooth… - Apple Community
I spent a good day into the night trying to set up and fix this.
So I have the same problem as this person, and I contacted Apple through Chat and then by phone, talked for quite a while over how this could be fixed, but since it's low priority on known bugs and so on, I decided to tinker around with a separate solution.
Since it works through the headphone jack, I posited that perhaps the problem is how the Application, Music handles Bluetooth, since my bluetooth works through Firefox and other Applications, such as Chess (also designed by Apple, BTW).
So I bought a Bluetooth 5.3 Adapter for Airplane to 2 Wireless Headphones, plugged it into the headphone jack, connected the headphone adapter to TX and then connected my headphones to the adapter and now Home Sharing works.
I'm aware this might seem like an imperfect solution, but it is a load better than nothing. Plus this might give some clues to the programmers at Apple to find a more permanent solution. Something in the homesharing to bluetooth code is messed up, but perhaps if you try to look at the headphone jack code for comparison or why it's able to externalize to a different bluetooth connection device it might help? Maybe.
Anyway, I hope this helps other people stuck in the same lurch as me and Apple Support. Skinny chance to the programmers too.