I run a mini jack cable from the TV headphone socket
[which cuts off the internal crappy tinny speaker]
to a low price good enough sounding
Behringer HA400 4 channel stereo headphone amp.

https://www.google.com/search?q=behringer+ha400&sxsrf=ALeKk00375jalWx5QJhCLFmhDu8MBXCd8g:1606380083584&source=lnms&tbm=shop&sa=X

One channel is permanently connected to a reasonable set of powered speakers
and sub bass,
for normal listening.

Then when the wife goes to bed I switch that off, and plug in headphones on a long cable.

I've not experimented with plugging a bluetooth transmitter into one of the spare headphone channels.

[I've never fancied wireless headphones for various reasons..]

But it is a potential option if would work ok...???