Is the device showing up in the device manager ?
Do you select it as audio output device in Windows audio settings loudspeakers configuration ?

CC stands for class compliant
Theoretically there is no reason why edge sound not comes thru.

Without the UCX connected the sound of the Edge browser comes thru the computer loudspeakers normal ?

With CC, the mode that is not working, there are actually only 2 inputs and 2 outputs.
So I wouldn't say it's a bad multi-channel implementation.

Switching back to USB brings back the sound in Edge.

The UCX II does not have a 2 in 2 out CC mode. See manual chapter 33.2. Lowest one is 8 channel I/O. And most probably you did not select any CC mode (in the OS, not the app) but use the default with 20 channels.

Windows UAC-2 mode does not work with multi-channel interfaces having more than a handful of these. That is a known and irrelevant limitation - we do have Windows drivers. If you want to know what's present and working in CC mode - a Mac will tell you.

Also when I commented on selecting the right CC mode I was thinking of your desired Linux application, not Windows.

I know but I cannot afford breaking the USB port just to switch to/from CC mode.
There are other ways to make this change without having to physically disconnect the USB port.

Why don't you implement them?

+1

Months ago I requested RME to modify the firmware providing us with an Offline feature to avoid physical disconnection of the USB cable when switching from USB to CC mode without turning off or putting the computer to sleep. I will not insist anymore.

My empathy to OP is because as an end User I want to use the options of my hardware as I choose and not as the manufacturer designs them (I know, someone must set the limits, otherwise it would be crazy), so IMHO here is the debate:

Design the features to force the User to use them as we decide or design based on how User wants to use it?

... I don't have the answer, I don't design hardware and I don't know what it means to serve customers in the most reliable way, I'm also sure that it must be difficult or impossible to create features via code that the hardware (maybe) has not been designed for ... BUT I know what I want as an End User.

My conclusion today is that I have one of the most versatile desktop audio interface on the market (the price proves it), a demonstration of real tech-evolution but I have to disconnect the USB cable to enjoy its versatility, so my best wishes to RME to keep improving the balance between your Creativity and our Wishes.

All the best