To be honest neither is slack. They've got push notifications through web service workers. What for would they need aggressive background activity?
I'm not saying this to be pedantic, just trying to nip this entitled vendor mentality in the bud. "We're important so give give give without asking." It's a bit what you see with permissions on mobile: the more famous a company is, the more brazen a permission policy they can get away with. It's only tangentially related actual functionality of the app.
This is not about you personally, by the way, but about vendors. You just shouldn't let them get away with it. Even if they're slack :)
The user ultimately needs to retain control. And I'm especially interested in the exception for audio - that really should be user-controllable, otherwise it just encourages annoying page authors to be even more annoying.
The audio thing works because there is an obvious icon in the tab bar that shows the source of audio, so if developers use it in an annoying way the user can easily respond appropriately.
There is now an incentive to do this, so it will happen. Same as "with popup blockers everywhere, popups are now replaced with HTML5 above-content layers."