Out of the box, Elevated Site Search indexes posts and pages. To search more content types (WooCommerce products, docs, or any public post type), add them under Elevated › Site Search › Settings › Advanced Options › Content to Index › Post Types and save. The index rebuilds automatically when the scope changes.
Navigate to Elevated › Site Search › Settings, expand Advanced Options, and locate Content to Index.

Open the Post Types selector and add every content type visitors should find. Any public post type on your site appears here, including ones registered by plugins, such as WooCommerce products.
Click Save Settings. Changing the scope triggers an index rebuild automatically; on most sites it finishes within a minute or two, and search keeps working while it runs.
Once the rebuild completes, results from the new post types appear in the search box, each with its own post type badge. In the Modern theme they are also grouped by type:

If your agent is connected (see Connect Your AI Agent), you can skip the steps above:
Index products and docs in addition to posts and pages, and tell me how many documents the index holds afterwards.
The agent widens the scope, waits for the automatic rebuild, and reads the document count back to you.
A post type isn’t offered in the selector. Only public post types can be indexed. Post types registered as private or excluded from search by their plugin do not appear.
New results are missing right after saving. The rebuild may still be running. Check the status line under Advanced Options › Indexer.