My late wife used to use Bluetooth headphones to listen to television. That seemed to work well for her, and myself as well, as she no longer had to play the TV at high volume to not struggle to hear it. There were no delay issues with the Bluetooth device she was using. although I kind of recall you had to make sure the device you purchased didn’t have that problem.
Later on she needed to get hearing aids. The hearing aids were able to directly receive Bluetooth signals so the headphones were no longer needed. However she said the sound of those, although loud enough, sounded tinny when listening via Bluetooth. So she stuck with the headphones. The hearing aids were expensive top of the line Siemens models that must not have been designed by audiophiles.
Mike