Good info, that means all sounds are broken. At least it's a consistent state (rather than one sound working and the other not).
The first thing I'd check for is that you can access the click sounds directly in the media path of your application. For example:
(But of course use your own application, not blockly-demo.)
I'd assume that if the sound files can't be loaded, then it would show up as a 404 in the console, and not a 'supported source' error. Nonetheless, it's the first thing to check.
The second thing I'd try is loading it in Firefox. The error you quoted appears to be from Chromium, so getting a second opinion would help determine if it's specific to the browser, or something more general.
Third, I'd look at the network tab in your browser's console. Is it ever attempting to load the sounds?
I'm not familiar with React, so I don't know if there are additional complications when playing sounds. Maybe someone else can chime in with that. All Blockly is doing is calling 'play()' on the sound.