You could give Runescape a go, since most of the "music" is pretty much just ambience in the background and doesn't need to be overly focused on the game, it likely works as a time sink to keep your hands busy at a relaxed pace while wanting to listen to / watch things.
Compared to other MMOs it is probably the most suitable / safe one for playing in the background / afking on. So if not objecting to using an MMO for this task it would probably be one of the better options. One issue would be that it would require a bit of time maybe an hour or so to get it into that situation though, getting past the tutorial and getting to somewhere where you can afk farm at compared to other games like people mentioned Binding of Isaac and the like where you can jump right into it from game installation and not need to faf about at all. But those games to require more attention and I personally find I tend to miss a lot of the thing I'm trying to listen to when playing a game that requires more attention. But of course if you are the type of person that can multitask well and pick up everything on the podcast while doing something more energetic and lively, then it might be good for you.