Typical SONY shit.
It's really unfortunate. I had the Sony pulse headphones prior to my 2015 bravia, at least I can use the 3.5mm out+the dongle for wireless.
FWIW my LeEco 55" outputs BT audio on all inputs. it's great
You can't pair them with a PS4 either.
Sony used to make some good crt's...not so much flat screens.
Shit like this is why I bought my last Sony product in 2001. Suck it Sony.
Most TVs don't do BT audio out. I wish it would be added and it was rumored to be in the works for Android 6 but was removed by google at the last minute. (At least that's the story I got).
However, There are a lot of BT transmitters on the market that will make your headphones pair easily.