Switch Audio Output depending on Display Output? Associate with saved Display profile?

I have a Steam Deck that I move often between 2 displays. One is a TV, so when I dock it I can use the TV Speakers. The second is a computer monitor that does NOT have speakers, but Audio settings switch to the monitor, so, the audio goes away. I then have to manually change Audio Output back to the Steam Deck to have audio.

I see there is an option in Display Configuration to “Save display properties: Only for this specific display arrangement”. Is there a way to persist Audio output preference depending on the current Display output?