[CodeHealth] Convert c/b/e/api/file_system to use modern callback

Bug: 1152279
Change-Id: I2f756aa39fb0d886aa6bb3df0a5949abc0d330ed
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/2652789
Reviewed-by: Sam McNally <sammc@chromium.org>
Commit-Queue: Maksim Moskvitin <mmoskvitin@google.com>
Cr-Commit-Position: refs/heads/master@{#848073}

chrome/browser/extensions/api/file_system/file_system_apitest_chromeos.cc

@@ -124,9 +124,9 @@ class FileSystemApiTestForDrive : public PlatformAppBrowserTest {
 
     ASSERT_TRUE(test_cache_root_.CreateUniqueTempDir());
 
-    create_drive_integration_service_ =
-        base::Bind(&FileSystemApiTestForDrive::CreateDriveIntegrationService,
-                   base::Unretained(this));
+    create_drive_integration_service_ = base::BindRepeating(
+        &FileSystemApiTestForDrive::CreateDriveIntegrationService,
+        base::Unretained(this));
     service_factory_for_test_.reset(
         new drive::DriveIntegrationServiceFactory::ScopedFactoryForTest(
             &create_drive_integration_service_));