Ensure that filtered notifications are removed from BadgeInfo.

There are cases where a BadgeInfo can contain a key that is later
used for a notification that should be filtered out. So instead
of simply not sending filtered notifications to PopupDataProvider,
now we explicitly send them and remove the corresponding key from
the BadgeInfo if it exists.

Bug: 35239510
Change-Id: I9532f47b1f07b44234f8707657b15b0de519b347