Search result links to prior version of a moved document
## Details

* Read the Docs project URL: https://hark.readthedocs.io/en/latest/

## Expected Result

Searching for "Portfolio" gets a top result which is this page:

https://hark.readthedocs.io/en/latest/example_notebooks/ConsPortfolioModel.html

## Actual Result

Searching for "Portfolio" gets to a 404 page:
https://hark.readthedocs.io/en/latest/example_notebooks/ConsPortfolioModelDoc.html

## Background information

- In this case, ConsPortfolioModelDoc was the name of the desired document in a previous version.
- The .rst documents point to this document via a symlink, which has been updated.
- A local sphinx build of the documentation gets the expected search result
diff --git a/readthedocs/projects/tasks.py b/readthedocs/projects/tasks.py
index fbd822300..cd27a64e5 100644
--- a/readthedocs/projects/tasks.py
+++ b/readthedocs/projects/tasks.py
@@ -1104,11 +1104,14 @@ class UpdateDocsTaskStep(SyncRepositoryMixin, CachedEnvironmentMixin):
                 epub=epub,
                 delete_unsynced_media=delete_unsynced_media,
             ),
-            callback=sync_callback.s(
-                version_pk=self.version.pk,
-                commit=self.build['commit'],
-                build=self.build['id'],
-            ),
+        )
+
+        # All the JSON files are uploaded to storage prior to syncing
+        # so we should be fine to index the files without waiting
+        sync_callback.delay(
+            version_pk=self.version.pk,
+            commit=self.build['commit'],
+            build=self.build['id'],
         )
 
     def setup_python_environment(self):
['readthedocs/projects/tasks.py']