[Code Health] Remove uses of base::SupportsWeakPtr. (sync)

This CL removes a use of base::SupportsWeakPtr from SyncableService
abstract base class by:

1. Adding a pure virtual function to return a base::WeakPtr.
2. Adding base::WeakPtrFactory class instances to the deriving
classes, if they don't already have one.
3. Implementing the function in the derived classes.

In most cases, leaf classes that have WeakPtrFactory instances are
marked as final for safety. However, there are some cases where test
classes extends some production classes, so they are not marked as
final. This can be fixed by expanding the class hierarchies, but that
adds more work and complexity, so I didn't pursue that.

Bug: 100114, 647430
Change-Id: Ia1e39071fd28130c8ea84e2282928350ddb43f9f
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5165864
Commit-Queue: David Bertoni <dbertoni@chromium.org>
Reviewed-by: Ted Choc <tedchoc@chromium.org>
Reviewed-by: Marc Treib <treib@chromium.org>
Code-Coverage: findit-for-me@appspot.gserviceaccount.com <findit-for-me@appspot.gserviceaccount.com>
Cr-Commit-Position: refs/heads/main@{#1243158}

• chrome/browser/ash/app_list/app_list_syncable_service.cc[diff]
• chrome/browser/ash/app_list/app_list_syncable_service.h[diff]
• chrome/browser/ash/app_list/arc/arc_package_syncable_service.cc[diff]
• chrome/browser/ash/app_list/arc/arc_package_syncable_service.h[diff]
• chrome/browser/extensions/api/storage/sync_storage_backend.cc[diff]
• chrome/browser/extensions/api/storage/sync_storage_backend.h[diff]
• chrome/browser/extensions/extension_sync_service.cc[diff]
• chrome/browser/extensions/extension_sync_service.h[diff]
• chrome/browser/spellchecker/spellcheck_custom_dictionary.cc[diff]
• chrome/browser/spellchecker/spellcheck_custom_dictionary.h[diff]
• chrome/browser/themes/theme_syncable_service.cc[diff]
• chrome/browser/themes/theme_syncable_service.h[diff]
• components/history/core/browser/sync/delete_directive_handler.cc[diff]
• components/history/core/browser/sync/delete_directive_handler.h[diff]
• components/search_engines/template_url_service.cc[diff]
• components/search_engines/template_url_service.h[diff]
• components/supervised_user/core/browser/supervised_user_settings_service.cc[diff]
• components/supervised_user/core/browser/supervised_user_settings_service.h[diff]
• components/sync/base/weak_handle_unittest.cc[diff]
• components/sync/model/syncable_service.h[diff]
• components/sync/model/syncable_service_based_bridge_unittest.cc[diff]
• components/sync/test/fake_sync_api_component_factory.cc[diff]
• components/sync/test/fake_sync_engine.h[diff]
• components/sync_preferences/pref_model_associator.cc[diff]
• components/sync_preferences/pref_model_associator.h[diff]