The TV manual isn't clear if the analog audio output of the TV can be used with the TV speakers turned on.
If you turn "speaker link" off in the sound menu of the TV then the TV speaker and headphone jack will definitely work at the same time.
You can connect a bluetooth transmitter to either the analog audio output (which can be set to a fixed level) or to the headphone jack (that will be a variable output). Either way the headphones will have their own volume control that may be completely independent of the TV volume or at least can be raised up above the level of the TV independently.