One other thing to try: https://addons.mozilla.org/firefox/addon/video-downloadhelper (presumably also available for other browsers). Then hold shift while you reload the page, and play the media. Chances are extremely good the addon will catch it and start dancing in your toolbar. Open the addon, click the file you want to download, and it should just download.

Open up developer console (F12) network tab and reload page/play audio. In the list of network requests, look for something that looks like the resource you want (e.g. in this case, filename: "mp3", initiator: "media", type: "mpeg"), right-click and "save response as". This doesn't work on every site, but works on yours!

Fancier sites do not serve media files directly but fetch encoded chunks of data and recombine them using javascript. To get the whole file back you need to re-implement the javascript, which is what yt-dlp does, but only works for sites it knows how to handle.

Just view the source code and search for ".mp3", the file is linked directly.

On Windows, you can use "Stream What You Hear" to "Record What You Hear". Any audio your computer plays can be recorded in real time with this app.