The short explanation
48kHz is the standard for video content. 96kHz and 192kHz appear on high-resolution releases. Higher rates carry more data and need more bandwidth.
Where you run into it
The rate is declared per format in the capability data, which is why a chain can support TrueHD at 48kHz and not at 192kHz. A source will then send the lower rate without comment.
The trap worth remembering: Atmos over ARC requires a cable that supports 192kHz audio. A cable can carry 600MHz video perfectly and still fail the audio return — which makes it look like a device fault rather than a cable one.
How the DR HDMI 8K handles it
Each of the DR HDMI 8K's audio flags carries its own sample rate control: L-PCM up to 192kHz with a bit width setting, TrueHD, DD+ and DTS-HD MA each with their own rate setting, as does one-bit audio. The EDID readouts show the advertised PCM capability including its rate and bit width.
Want to test your own HDMI chain?
The DR HDMI 8K is sold through the HDFury.eu web shop.