Share your experience!
Oh it’s doable, and Sony do it - but not at your price point.
It’s easy to overcome, though with a £25 Bluetooth transmitter with Optical In, of which Amazon offer several.
So I guess Sony are willing to alienate a lot of surprised customers for its lower-end sets for whatever fraction of that £25 it would cost Sony to build it in 😢
I also hear tell of a free Bluetooth app you might be able to find on the Android TV Store that can add this missing profile, but I don’t know if your TV has the fundamental hardware needed. Worth investigating, though.