Yeah hi lmao
Sorry I forgot that most people tend to just leave the Global Audio Devices as per the OBS defaults. Let me reiterate. It DOES mute the sound if you disable every audio device in your OBS Settings and only add them as individual sources within your scenes. That way when you shift Scenes, the sources simply are not on the current scene, so OBS just shuts them all down. I prefer to set OBS audio up this way so that I have tighter control over what audio is and isn't allowed on certain scenes.
So, if you set up a black scene with nothing on it (you've probably seen me do this from my transition from fanart slideshow to my intro video) it will deactivate everything with one button press. It will always take a second for every source from the previous scene to deactivate, but the visual effect is pretty immediate. I have a completely blank Scene with only the device I output Foobar to for capture, so I can fade the music out manually using that Scene + Fade Transition. Pain in the ass but better than nothing.