[Fallback Icons] Refactor FallbackIconService to be a BrowserContext-level singleton

chrome/browser/favicon/DEPS

 include_rules = [
   # Favicon is being made into a Browser Component, so we have these
   # three basic rules followed by temporary exceptions.  Please don't
   # add to the list of exceptions!
   "-chrome/browser",
   "+chrome/browser/chrome_notification_types.h",
   "+chrome/browser/common",
   "+chrome/browser/favicon",
 
   # Permanently-allowed DEPS beyond the standard Browser
   # Components-like DEPS above go here.
   "+chrome/browser/profiles/incognito_helpers.h",
   "+chrome/browser/search/search.h",
   "+components/favicon/core",
+  "+net/base/registry_controlled_domains/registry_controlled_domain.h",
   "+third_party/skia/include/core/SkBitmap.h",
 
   # TODO(caitkp): Bring this list to zero.
   #
   # Do not add to the list of temporarily-allowed dependencies below,
   # and please do not introduce more #includes of these files.
   "!chrome/browser/bookmarks/bookmark_model_factory.h",
   "!chrome/browser/history/history_backend.h",
   "!chrome/browser/history/history_service.h",
   "!chrome/browser/history/history_service_factory.h",
   "!chrome/browser/history/select_favicon_frames.h",
   "!chrome/browser/profiles/profile.h",
   "!chrome/browser/ui/webui/chrome_web_ui_controller_factory.h",
   "!components/bookmarks/browser/bookmark_model.h",
   # Do not add to the list of temporarily-allowed dependencies above,
   # and please do not introduce more #includes of these files.
 ]
 
 specific_include_rules = {
   # Browser tests, by definition, need access to the browser objects.
   '.*_browsertest\.cc': [
     "+chrome/browser",
   ]
 }