PasswordSyncBridge: Stop using SyncMetadataStoreChangeList::TakeError()

SyncMetadataStoreChangeList::TakeError() is deprecated - this pattern
makes it too easy to accidentally forget to check for an error.
This CL migrates PasswordSyncBridge (the last user of TakeError()) to
the new pattern, which is passing an error callback to the
SyncMetadataStoreChangeList.
A followup CL will remove TakeError().

Bug: 40860762
Change-Id: I4dfd7887cc26e8c0ae88d4eca9cae4949c942b54
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5397879


Reviewed-by: Jood Hajeer <jood@google.com>
Commit-Queue: Marc Treib <treib@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1278926}