I don’t think you’re going to find a solution to this in any shape or form. The mute function in the TV or soundbar is linked with the volume control. You want a constant volume output to the TV Connector so you can have independent volume control relative to the speakers. However, there is no mute in this sound path. There’s not technical reason they couldn’t mute this sound path as well, but absolutely NOBODY does this (in terms of TV manufacturers).
The only way you could “piggyback” off the speaker output mute function is to get a volume-controlled output from the TV which would be even more frustrating because you’d have to adjust your volume every time your partner adjusted the speaker volume and you might easily run out of range one way or the other.