Refactor BackupManagerService to use UserManagerInternal

Replace the usage of the public `UserManager` API with the
internal `UserManagerInternal` service within BackupManagerService.
This aligns with common practice for core system services interacting
with user management and allows access to internal helper methods.

Also remove the unused getContext() method.

Test: atest com.android.server.backup.BackupManagerServiceTest
Test: atest com.android.server.backup.BackupManagerServiceRoboTest
Test: atest com.android.server.backup.UserBackupManagerServiceTest
Test: atest com.android.server.backup.keyvalue.KeyValueBackupTaskTest
Test: atest com.android.server.backup.internal.SetupObserverTest
Bug: 406114361
Flag: EXEMPT refactoring
Change-Id: Ia43f28c2426fc146e37dea08bb714464a2f17b93