waffle: Introduce SearchEngineChoiceService::Client

It is an intermediary between the service and some of its dependencies
that live in `//chrome` layer or have a lifecycle that would otherwise
not allow injecting them in the service at construction time.

This CL uses this to stop storing guest DSE propagation eligibility in
the service, instead resolving it as needed. It allowed flagging some
dead code & irrelevant remaining tests

OBSOLETE_HISTOGRAM[Search.SaveGuestModeEligible]=Not useful now that the feature is fully launched

Bug: 404176285,410878553
Change-Id: I25a02aca625fa86255b6d2396ae47cf186186733
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6458470
Auto-Submit: Nicolas Dossou-Gbété <dgn@chromium.org>
Reviewed-by: Marc Treib <treib@chromium.org>
Reviewed-by: Jérôme Lebel <jlebel@chromium.org>
Commit-Queue: Nicolas Dossou-Gbété <dgn@chromium.org>
Reviewed-by: Tomasz Wiszkowski <ender@google.com>
Cr-Commit-Position: refs/heads/main@{#1450461}