Switch to a non-hidden way to compute data path and switch to subdir.

We need to store other things in the appsearch data dir other than what
Icing stores, such as the storage info cache.

Bug: 177685938
Bug: 181787682
Test: Presubmit
Change-Id: I903c34a2c891d617217d44f5126d0d31c8c6bf39