Currently, I see double popup notifications in some cases when I have multiple tabs / browser windows open.

This already shouldn't happen, so there's likely some sort of bug in the synchronization code, but after T12563 we'll routinely expect duplicate messages to be a possibility and the synchronization primitives we have to work with are inherently a bit questionable.

Making the client robust to duplicate notifications is comparatively easy and reliable, and will give us more leeway to make better choices elsewhere (for example, synchronization can err on the side of allowing duplicate notifications through).

(Ideally, we should also hunt down the sync bug which causes this, of course.)