While the vast majority of current TVs, sound systems and stereos offer audio reception via Bluetooth, they cannot send Bluetooth audio. A Bluetooth headset as a pure playback system must of course receive audio, otherwise, there is radio silence.
If you are looking for a device with which you can pair Bluetooth headphones, you should therefore check whether the integrated Bluetooth interface can send audio. The Bluetooth logo on the packaging or in the TV's manual is usually not enough.
If the device does not offer this function, it can be upgraded with a Bluetooth transmitter.
There are various Bluetooth transmitters available in stores. The connection is always the same: If the output device (e.g. TV or sound system) has a free sound output such as a headphone output, the adapter can be connected here.
More information can be found here Bluetooth headphones on the TV.