Update release process doc for auto-docs push (nginx#2509)

The docs workflow now supports automatically deploying docs. This updates the release process doc explaining how to set that up.

Author: miledxz

docs/developer/release-process.md

@@ -66,7 +66,7 @@ To create a new release, follow these steps:
     4. `GW_API_PREV_VERSION` in tests Makefile, if necessary.
     5. Any references in the docs to the previous release.
     6. Any installation instructions to ensure that the supported Gateway API and NGF versions are correct. Specifically, helm README.
-8. Run the [docs workflow](https://github.com./nginxinc/nginx-gateway-fabric/actions/workflows/docs-build-push.yml) for **prod** on the **release branch**.
+8. Run the [docs workflow](https://github.com./nginxinc/nginx-gateway-fabric/actions/workflows/docs-build-push.yml) for **prod** on the **release branch**. Open a PR to the release branch to turn auto-deploy on for the docs workflow in this branch. See [this README](https://github.com./nginxinc/docs-actions/tree/v1.0.4?tab=readme-ov-file#caller-example) for how to do this. Docs should only be auto-published when changes to the `site/` directory are made.
 9. Close the issue created in Step 1.
 10. Ensure that the [associated milestone](https://github.com./nginxinc/nginx-gateway-fabric/milestones) is closed.
 11. Verify that published artifacts in the release can be installed properly.