[Connector API][Doc] Add info about required privileges (#3721) (#3748)

* [Connector API][Doc] Add info about required privileges

* Update docs/overlays/elasticsearch-shared-overlays.yaml

Co-authored-by: Liam Thompson <[email protected]>

---------

Co-authored-by: Liam Thompson <[email protected]>
(cherry picked from commit bce4f27)

Co-authored-by: Jedr Blaszyk <[email protected]>

Author: github-actions[bot]

docs/overlays/elasticsearch-shared-overlays.yaml

@@ -36,6 +36,8 @@ actions:
             Connectors are Elasticsearch integrations for syncing content from third-party data sources, which can be deployed on Elastic Cloud or hosted on your own infrastructure.
             
             This API provides an alternative to relying solely on Kibana UI for connector and sync job management. The API comes with a set of validations and assertions to ensure that the state representation in the internal index remains valid.
+
+            This API requires the `manage_connector` privilege or, for read-only endpoints, the `monitor_connector` privilege.
           externalDocs:
             url: https://www.elastic.co/guide/en/elasticsearch/reference/master/es-connectors-tutorial-api.html
             description: Check out the connector API tutorial