[searchprefetch] Simplify getting search terms's logic

When calling HasCanonicalPreloadingOmniboxSearchURL, it calls
GetDefaultSearchProvider()->ExtractSearchTermsFromURL
to extract the search terms already, and the result can be shared
via an output param, so we do not need to calculate the terms again.
This CL simplifies the logic.

Bug: 413557424
Change-Id: I75b113347e08e890dfafbc324e4c3881d7aad487
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6518716
Reviewed-by: Hiroki Nakagawa <nhiroki@chromium.org>
Commit-Queue: Lingqi Chi <lingqi@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1456860}