@statements
Not from Sony, but on Amazon, and no doubt in many other places, you will find Bluetooth transmitters that connect to the S/PDIF digital out on the back of the TV.
Pick one with low latency, within the confines of whatever Bluetooth codecs your headphones support, and ensure that the TV is putting out a signal of suitable strength on the digital out, and you should be good to go.
Using optical doesn’t necessarily mute the TV speakers; if you want this, some further digging in the manual
https://www.sony.com/electronics/support/res/manuals/Z012/Z012721111.PDF
may be required.
Good luck!
My favourite bedtime reading is a Sony product manual…
