Switch browser/extensions/api/file_system/file_system_api.[h|cc] to the TaskScheduler API

chrome/browser/extensions/api/file_system/file_system_api.h

Index: chrome/browser/extensions/api/file_system/file_system_api.h
diff --git a/chrome/browser/extensions/api/file_system/file_system_api.h b/chrome/browser/extensions/api/file_system/file_system_api.h
index 740c44706c185d021514b170b0a882f33a68cc4e..7c5a99d724eca80872502b5089a0ea84f10dba66 100644
--- a/chrome/browser/extensions/api/file_system/file_system_api.h
+++ b/chrome/browser/extensions/api/file_system/file_system_api.h
@@ -13,6 +13,7 @@
 #include "base/files/file_path.h"
 #include "base/macros.h"
 #include "base/memory/weak_ptr.h"
+#include "base/task_scheduler/post_task.h"
 #include "base/values.h"
 #include "build/build_config.h"
 #include "chrome/browser/extensions/chrome_extension_function.h"
@@ -157,7 +158,7 @@ class FileSystemEntryFunction : public ChromeAsyncExtensionFunction {
  protected:
   FileSystemEntryFunction();
 
-  ~FileSystemEntryFunction() override {}
+  ~FileSystemEntryFunction() override;
 
   // This is called when writable file entries are being returned. The function
   // will ensure the files exist, creating them if necessary, and also check
@@ -187,6 +188,11 @@ class FileSystemEntryFunction : public ChromeAsyncExtensionFunction {
 
   // Whether a directory has been requested.
   bool is_directory_;
+
+  // The task runner used to do file operations.
+  const scoped_refptr<base::SequencedTaskRunner> task_runner_ =
+      base::CreateSequencedTaskRunnerWithTraits(
+          {base::MayBlock(), base::TaskPriority::BACKGROUND});
 };
 
 class FileSystemGetWritableEntryFunction : public FileSystemEntryFunction {