Move lagging users over to new storage API.

Over the last month we've been moving everyone over to the new
StorageStatsManager public APIs, but we missed these users.

The ApplicationsState changes are straightforward, but we had to
completely rewrite StorageMeasurement to use the new fast-path
quota APIs.

Test: builds, boots, UI using StorageMeasurement works.
Bug: 36056120
Change-Id: If02177c95bf8c96ae4eceac4d631a168f99bef84