Migrate Extensions code to Task Scheduler API

extensions/browser/api/storage/local_value_store_cache.cc

Index: extensions/browser/api/storage/local_value_store_cache.cc
diff --git a/extensions/browser/api/storage/local_value_store_cache.cc b/extensions/browser/api/storage/local_value_store_cache.cc
index ef91d20d58abc7ef8ed0782bdd79a0f670946a6c..a1e03b9155cf019f67aca7fddb1ec86acfd84e7a 100644
--- a/extensions/browser/api/storage/local_value_store_cache.cc
+++ b/extensions/browser/api/storage/local_value_store_cache.cc
@@ -9,6 +9,7 @@
 #include <limits>
 
 #include "content/public/browser/browser_thread.h"
+#include "extensions/browser/api/storage/backend_task_runner.h"
 #include "extensions/browser/api/storage/weak_unlimited_settings_storage.h"
 #include "extensions/browser/value_store/value_store_factory.h"
 #include "extensions/common/api/storage.h"
@@ -39,13 +40,13 @@ LocalValueStoreCache::LocalValueStoreCache(
 }
 
 LocalValueStoreCache::~LocalValueStoreCache() {
-  DCHECK_CURRENTLY_ON(BrowserThread::FILE);
+  DCHECK(IsOnBackendSequence());
 }
 
 void LocalValueStoreCache::RunWithValueStoreForExtension(
     const StorageCallback& callback,
     scoped_refptr<const Extension> extension) {
-  DCHECK_CURRENTLY_ON(BrowserThread::FILE);
+  DCHECK(IsOnBackendSequence());
 
   ValueStore* storage = GetStorage(extension.get());
 
@@ -61,7 +62,7 @@ void LocalValueStoreCache::RunWithValueStoreForExtension(
 }
 
 void LocalValueStoreCache::DeleteStorageSoon(const std::string& extension_id) {
-  DCHECK_CURRENTLY_ON(BrowserThread::FILE);
+  DCHECK(IsOnBackendSequence());
   storage_map_.erase(extension_id);
   storage_factory_->DeleteSettings(settings_namespace::LOCAL,
                                    ValueStoreFactory::ModelType::APP,