Add a test for the WebDataServiceBase::Init error callback

The logic for this may be subtly changing in a future CL, so
this CL adds a test to verify that no regressions are introduced.

This was not tested directly before.

BUG=40267945

Change-Id: I9a66324daf40c00034c88a4daa99b1bf753b0771
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5827798


Commit-Queue: Will Harris <wfh@chromium.org>
Reviewed-by: Peter Kasting <pkasting@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1349506}