As you can see in the video I can apply the custom CSS without problems, once I want to use the custom CSS with a class it doesn’t apply the changes. I also tried to apply the styling of the class in the child theme. But it still doesn’t work.
There are some default styles on the audio element which are more specific than your custom class. Instead of just root { ... } please use root.brxe-audio { ... } instead to make the selector more specific.