Handle EXTRA_KEY_REQUEST_WRITE_REPAIR_MODE_PW

So the new password can be saved per caller's request.

This will remove the additional step to ask the user
to enter the new credential again and thus simplifying
the UI flow.

Bug: 271968977
Bug: 277561275
Test: atest SettingsUnitTests:SaveAndFinishWorkerTest
Test: atest ChooseLockPasswordTest
Change-Id: I20232619225b17edda0a72dad43b120d5a249203