If you don’t have native BT on your TV (and it sounds like you don’t) and if you SmartTv stick doesn’t support BT, then you can buy a BT dongle that attaches to the audio-out jack on your TV. Then just pair your BT headphones to that dongle and you are good to go.
There are about a billion options on Amazon…
https://www.amazon.com/TaoTronics-Bluetooth-Transmitter-Receiver-Simultaneously/dp/B01EHSX28M