This device?
That device plays audio from your smartphone or laptop to connected speakers. You want a BT transmitter, but the problem you'll have is finding one compatible with your TV. It's difficult enough finding Windows drivers for these BT transmitter dongles. Plus you would need a tool on the TV to pair with your earbuds.
Sennheiser have
"wireless" earbuds if you don't want headphones.
Personally, I used a long 3.5mm cable to wired headphones,
Philips X2HR. The TV has enough power to drive them, large comfortable earcups, you can wear for ours. I have a
Fiio A3 headphone amp but don't need it.