I did some quick tests.
I pressed the play button and the file downloaded as you described.
I renamed the downloaded filename and added the .m3u extension and then dragged that onto the Firefox address bar.
Firefox then asked me if I wanted to save the file or open an application.
If I selected VLC, VLC was opened and the channel played.
I tried the same experiment with MS Edge and it just downloaded the file.
There was an 'open file' option and that loaded MS Media Player.
Back to Firefox, 'open file' from the downloads list also opened MS Media Player.
Chromium under Linux complained about http not being secure, but eventually downloaded the file.
Firefox under Linux also complained about insecure http but eventually downloaded the file.
So, if the name is changed from "c0d7eec39f43ef8670e49c05a9613e2a" to "c0d7eec39f43ef8670e49c05a9613e2a.m3u", Firefox will ask you what to do instead of downloading the file, unless you also select "Always do this", in which case I assume that Firefox will just open the default app that you set.
I also tried dragging the renamed file onto Edge but it just downloaded the file again.
Once I had done all that, I tried with Firefox again. This time it recognised the file as an m3u automatically and asked what I wanted to do. When I selected VLC, it played.
Try:
Renaming the downloaded file with the extension .m3u, loading that into Firefox and selecting VLC.
After that, try just the 'Play' button alone and see if that works.
My Firefox settings now look like this:
If I change the action to "Use VLC media player", clicking "Play" launched VLC and plays the channel.
Please let the forum know if this worked.