The reason why you see those results is because the plugin re-directs to the default wordpress search page by default. The search cannot modify this page layout unfortunately because it's a theme feature.
However, what you are seeking is to redirect to the woocommerce search page, which is different from the default one. It's possible, and since you gave back-end details I made the change in the configuration, so now the search redirects to the correct woocommerce search page.
I've changed the Redirect to url? option on the General Options -> Behavior panel from
The additional parameter tells wordpress that you are seeking a product, and WooCommerce search takes the control automatically.Best,
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