Search results page for blog only
If "Enable live search for products and pages." option is not enabled in Flatsome>Advanced>Site Search, results page should be "search.php" instead of "archive-product.php". Some users use Flatsome just for blogging and Woocommerce only for login feature. They don't want to see "No products were found matching your selection." in search results page.
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Tommy Jacobs Vedvik