Seems like the current solution they're advocating for is for sites to do background processing in a [Worker][1].
This seems like a step towards the way things work with mobile apps currently, where the app's main thread gets suspended when its not in the foreground, and background processing happens in separate threads which the user has some degree of control over.
Edit: I meant regular `Worker`s, not `ServiceWorker`s.
[1]: https://developer.mozilla.org/en-US/docs/Web/API/Worker