Understood. My phone uses WiFi at home so I have no concern for the amount of data used.
I haven’t seen a radio since the 80’s that didn’t put out stereo on it’s headphone socket though, it might have one speaker but it will be putting out stereo on the headphone socket.
Moving the balance to the right will stop the radio sound in your left ear but will also drop all of the audio information carried in the left channel but not the right.
If you buy the two connectors suggested earlier in this topic put one in the radio and one in the TV connector V2 and then enable flight mode on your left hand HA, you would have everything that you want: both channels mixed together supplied to just your right HA.