Ensure clean shutdown of Local Storage in tests

Tests set up Local Storage in a temporary directory. If the directory
has opened files during test shutdown, temp directory deletion can fail
on Windows and cause test flake.

This properly reorders LocalStorageImpl's shutdown synchronization logic
so that we can ensure no LevelDB files remain open once the shutdown
callback is invoked.

Fixed: 1151226
Change-Id: Id9cad4ae8a305e12c965e1fb3d8908b739050cbc
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2617869Reviewed-by: Victor Costan <pwnall@chromium.org>
Commit-Queue: Victor Costan <pwnall@chromium.org>
Commit-Queue: Ken Rockot <rockot@google.com>
Cr-Commit-Position: refs/heads/master@{#841730}

components/services/storage/dom_storage/local_storage_impl.cc

@@ -1102,10 +1102,10 @@ void LocalStorageImpl::OnOriginsDeleted(leveldb::Status status) {
 void LocalStorageImpl::OnShutdownComplete() {
   DCHECK(shutdown_complete_callback_);
   // Flush any final tasks on the DB task runner before invoking the callback.
-  leveldb_task_runner_->PostTaskAndReply(
-      FROM_HERE, base::DoNothing(), std::move(shutdown_complete_callback_));
   PurgeAllStorageAreas();
   database_.reset();
+  leveldb_task_runner_->PostTaskAndReply(
+      FROM_HERE, base::DoNothing(), std::move(shutdown_complete_callback_));
 }
 
 void LocalStorageImpl::GetStatistics(size_t* total_cache_size,