Note the phrase preventing to start. Already playing media would be unaffected.

+: Also the rule would be extended to include minimized browser even if the tab is selected.

What does that even mean? You can't stop at a single file or stream as that would most likely still break things. If you allow tabs that play sound to continue to play sound you could just run a small, short, silent sound file on page load and then do whatever you want for the life of the tab.

I think you could mitigate the 'play short/silent sound on page load'. Each tab would have a max volume limit. The limit can be increased automatically while the tab is open, but it must stay within some % of that limit when the tab is not open. The default limit would be 0. You can add some restraints on the length of sound too, like require a sound to play for at least a second before adopting its new volume for the tab.