[Prefetch] Reorder the prefetch eligibility checks

In this CL, we reorder the eligibility checks for search prefetch to
check for search terms before checking other reasons.

We add new histograms to deprecate the old ones as we change
the ordering.

Bug: 1346344
Change-Id: If0fb1364d97bf8330433fb6a0ac26ccf16d2677a
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3780994
Reviewed-by: Ryan Sturm <ryansturm@chromium.org>
Reviewed-by: Tomasz Wiszkowski <ender@google.com>
Commit-Queue: Sreeja Kamishetty <sreejakshetty@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1030388}