[Sync] Convert DTCs to be not RefCounted and NonThreadSafe.

components/sync/BUILD.gn

Index: components/sync/BUILD.gn
diff --git a/components/sync/BUILD.gn b/components/sync/BUILD.gn
index 55b8e6d07993194bbc808723a07f42ef93fc57ce..45a2f52e9a7ff2d9e5221b61293a2da741fdeaa8 100644
--- a/components/sync/BUILD.gn
+++ b/components/sync/BUILD.gn
@@ -22,6 +22,9 @@ static_library("sync") {
     "api/conflict_resolution.cc",
     "api/conflict_resolution.h",
     "api/data_batch.h",
+    "api/data_type_error_handler.h",
+    "api/data_type_error_handler_impl.cc",
+    "api/data_type_error_handler_impl.h",
     "api/entity_change.cc",
     "api/entity_change.h",
     "api/entity_data.cc",
@@ -135,7 +138,6 @@ static_library("sync") {
     "core/data_type_association_stats.h",
     "core/data_type_debug_info_listener.cc",
     "core/data_type_debug_info_listener.h",
-    "core/data_type_error_handler.h",
     "core/delete_journal.cc",
     "core/delete_journal.h",
     "core/http_bridge.cc",
@@ -671,7 +673,8 @@ static_library("test_support_sync_core") {
 static_library("test_support_sync_core_impl") {
   testonly = true
   sources = [
-    "core/test/data_type_error_handler_mock.h",
+    "api/data_type_error_handler_mock.cc",
+    "api/data_type_error_handler_mock.h",
     "core/test/fake_model_type_connector.h",
     "core/test/fake_model_type_processor.h",
     "core/test/fake_sync_manager.h",
@@ -680,7 +683,6 @@ static_library("test_support_sync_core_impl") {
     "core/test/test_entry_factory.h",
     "core/test/test_internal_components_factory.h",
     "core/test/test_user_share.h",
-    "core_impl/test/data_type_error_handler_mock.cc",
     "core_impl/test/fake_model_type_connector.cc",
     "core_impl/test/fake_model_type_processor.cc",
     "core_impl/test/fake_sync_manager.cc",