I tried to analyse the audio source of the following podcast:
Yet, the Network tab does not show any traffic although “all” is selected – why?
Hi!
I tried the website you linked and I consistently see a request to a mp3 file when clicking on the play button. If you open the netmonitor before clicking on the play button for the first time, you should see the request as well.
I imagine the content is downloaded in chunks, and we don’t pick up the request if it was already sent and we are only receiving chunks. Typically Firefox DevTools only record requests when they are sent or when the response is received. I will file a bug to investigate this. For info, it looks like Chrome shows the request in such scenarios.
Edit: Filed https://bugzilla.mozilla.org/show_bug.cgi?id=1882023
Thank you for this very valuable information! 
Yes, it would be very helpful and useful if FF displayed chunks downloaded after the list of requests had been cleared/initialized.
It would be particularly useful if the initial web page request triggered dozens of requests, bloating the Network Monitor tab. The list could be cleared then and the chunks downloaded after that would still be displayed.
PS: Accidentally, I wrote “Auto” in the title. It should read “Audio”, of course. 