Refactor BackupManagerService activation logic

This change refactors parts of BackupManagerService, primarily focusing
on the logic that determines whether backup is active for a given user.
This serves as preparation for future changes.

Key modifications include:
- Introduced a new helper method `isDefaultBackupActiveUser(int userId)`
  to encapsulate the logic determining if a user's backup is initially
  set to active.
- Refactored the `isBackupActivatedForUser(int userId)` method to improve
  clarity and structure.
- Updated `activateBackupForUserLocked` and `deactivateBackupForUserLocked`
  to utilize the new `isDefaultBackupActiveUser` helper method.
- Updated `BackupManagerServiceTest` to mock the static call to
  `UserManager.isHeadlessSystemUserMode()` introduced by the refactoring.
- Replaced `mStateLock` with `mLock`.
- Added `@UserIdInt` annotations to `userId` parameters in numerous methods
  for improved code clarity and type safety.

Test: Existing tests in BackupManagerServiceTest updated and pass.
Bug: 374830726
Bug: 406114361
Flag: EXEMPT refactoring
Change-Id: If8134514a1b7e7c148c421e4dc96eb6d6e31c26e