[omnibox][zps] Encapsulate all caching inside ZeroSuggestCacheService.

Encapsulates all zero-suggest caching inside ZeroSuggestCacheService,
whether in-memory or pref-based. In addition to simplifying the code,
this allows the ZeroSuggestCacheService's observer model to be used by
Chrome Journeys without depending on launching the in-memory caching.

Bug: 1351224
Change-Id: I5fadf31347696703929552c0909e918ef4ddd7c9
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4544341


Reviewed-by: Sophie Chang <sophiechang@chromium.org>
Commit-Queue: Khalid Peer <khalidpeer@chromium.org>
Code-Coverage: Findit <findit-for-me@appspot.gserviceaccount.com>
Reviewed-by: Moe Ahmadi <mahmadi@chromium.org>
Reviewed-by: Joshua Bell <jsbell@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1149435}