You can buy devices to extract audio from an optical output, and even from HDMI - but only if it's an HDMI-ARC port, most modern TV's should have one that's specifically labelled ARC, if nit then there's no audio output (HDMI on a TV is obviously input only).
The tv has a HDMI-ARC port but if this option is chosen - will it enable the internal speaker to keep on playing?
The mute is done by mechanical switches in the jack. Of course, you might not want to do this but if you remove the rear cover, you can join the terminals to prevent this.
As I have shown in black.
View attachment 141203
Thanks, but I don't wish to make such an change unless there are no other options.