I would like to see the media player controller as a Firefox tool above the AI chat bot on the sidebar. It's very comfortable to switch music or pause videos while browsing the internet.
To have audio controls at sight in a fixed place would avoid the problem to be going away in the search of the audio-playing tab, specially when you have many tabs around... Indeed.
I guess the implementation could be general/universal, meaning, no matter how many audio-players are running in how many tabs, you can play/stop all of the at once -just in case you have more than one audio stream and so the control doesn't let some audio playing in cases of casual juxtaposition...
Anyway, good idea. Something very minimal, which controls play/pause/stop, and maybe go-forward/next-chapter|go-backwards/previous-chapter.