From what I understand, the end of the URL string is just one of the clues the browser uses to determine the "type" of received data (https://mimesniff.spec.whatwg.org/), and the true behavior depends on the browser's specific implementation. A part of the process involves actually reading and analyzing a small portion of the received file to see if the file really is the type that the URL claims it is. For example, I started a quick python server, and made it serve the OP image, except I renamed it as a jpg file (without actually converting the image of course). When saving the picture inside the browser, Firefox correctly identifies the file as a png image: While edge incorrectly tries to save the image as a jpg image:
Regarding your "MP3" file specifically, opening it in a hex editor reveals that the actual file contents identifies itself as an M4A file, despite what the URL claims:
So, you should be good to download them any way you find convenient, and then just renaming them to the proper extension afterwards.