How to get sound out to an AVR using HDMI

I have been struggling with this for a decade now. The actual monitor is hooked up to the GPU, in this case a 2019 Mac Pro using Thunderbolt to a Pro Display XDR.

Separately, I need the Dolby Atmos sound to go to an Audio Video Receiver via an HDMI 2.1 connection. Again from the GPU. No, I do not want that to be a monitor, I want it to be the sound playing device. In fact, it is not a monitor, it is an AVR.

Specifically I want the eARC input on the AVR used to exactly and only play sound.

If your solution involves an RCA jack, TOSLINK cable, ARC, or any other low resolution sound, you are not solving this issue. Dolby Atmos does not travel over low bandwidth connections.

I am willing to try the Apple media adapter yet again, but in the past it has failed at adapting. It will specifically not pass the sound. I have returned it at least 3 times so far. And anyway, the GPU has one HDMI out.

The complicating thing here is if the solution is to add the AVR as a 2nd monitor, then the GPU fails at feeding the Pro Display XDR its highest resolution. Which makes the $7k monitor useless.