Play music file while browsing movie lists,etc.

You can play an audio file and start browsing the list, but it's not an automated thing. You would need to file a feature request in Kodi forums to see what response it gets from core devs. Sounds horrible to me

mattIV Kodi is no multi-task OS. Media playback is the primary task by design. Use a regular OS, if you need background music.

I've been in a situation, where I would like to watch a live video stream (TV), but since it doesn't at the time contain any interesting content, I would like to listen something else instead of whatever audio is in the stream. But still, I'd like to see the video feed so that I can stop the music when the actual interesting broadcast starts.

So, I'd say there is another use case, but it's quite niche. I've though this is a first-world-problem and decided to live with it :-).

But, broadly speaking: "override current audio (from a video-including content) with some other audio source" (I haven't actually browsed a movie list, so I'm not sure on OPs issue, but I presume the issue here is a preview with audio?). How it could be done in UI, is one issue. The design is not trivial. Another issue is, how easy/difficult this is technically, and if it is worth the effort.

If you press the "TAB" key on your keyboard while an audio or video file is playing playback is backgrounded and you can navigate through menus. Pressing TAB again (or selecting "Full Screen" option in menu) will bring it to the foreground again.

You can also map that function to a button on your remote (it's the "FullScreen" kodi action).

so long,

Hias