Privacy Sandbox Settings: Fix threading for callback helper

Running the callback helper on the UI thread doesn't work when the
fledge callback is called asynchronously when the InterestGroupStorage
feature is enabled by default.
This change fixes a test failure in https://crrev.com/c/5041672.

Change-Id: I56e67b157eb08d852a9d000bb80604e2cc59fb6e
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5068360
Reviewed-by: Theodore Olsauskas-Warren <sauski@google.com>
Commit-Queue: Theodore Olsauskas-Warren <sauski@google.com>
Auto-Submit: Christian Dullweber <dullweber@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1231230}