BUG: Post doesn't update in Elasticsearch when "Post Search" is disabled

[burhandodhy]

Describe the bug

When the "Post Search" feature is disabled, updating a post does not sync the changes to Elasticsearch.

Steps to Reproduce

1. Go to the Features page and disable "Post Search".
2. Edit any post and make some changes.
3. Check the post in Elasticsearch and compare it with the updated content in WordPress.

Screenshots, screen recording, code snippet

No response

Environment information

No response

WordPress and ElasticPress information

No response

Code of Conduct

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