Storage Refactor: Rename similar objects in preparation for refactor

The addition of a storage abstraction allows us to shift
responsibilities across a few objects to better promote code health and
testability.

In particular, the obex client no longer needs to also store contacts,
and the service and state machine no longer both need to worry about
user unlocks and account readiness. The existing PullRequest completion
processors that own storage currently are now redundant.

This change moves several objects over in naming to make room for the
new implementations. Objects with name changes were too difficult to
edit in place with flagging. Other downstream objects have been marked
for removal with warning messages.

Bug: 365626536
Bug: 376461939
Test: atest com.android.bluetooth.pbapclient
Test: m com.android.btservices
Change-Id: I3b1ebd509a4ba56935a46d885d6972a1925a7313