Limit searches on the whole site to only show products.

product-search-only.php

<?php
/**
 * Product Search Only
 *
 * @package           AllowPrivacyPolicyPageEdits
 * @author            Bernhard Kau
 * @license           GPL-2.0-or-later
 *
 * @wordpress-plugin
 * Plugin Name:       Product Search Only
 * Plugin URI:        https://gist.github.com/2ndkauboy/011d8a28cdc462e61a4f0dacd48326eb
 * Description:       Limit searches on the entire site to only show products.
 * Version:           1.0.0
 * Requires at least: 4.9
 * Requires Plugins:  woocommerce
 * Author:            Bernhard Kau
 * Author URI:        https://kau-boys.de
 * License:           GPL v2 or later
 * License URI:       https://www.gnu.org/licenses/gpl-2.0.html
 */

/**
 * Redirects search queries to the product search results page.
 *
 * This function ensures that search queries on the site are redirected
 * to the WooCommerce shop page with the search parameter appended.
 * It prevents execution in the admin panel and avoids redirection
 * when already on the relevant product search pages.
 *
 * @return void
 */
function product_search_only_redirect_search_to_products() {
	if ( is_admin() ) {
		return;
	}

	if ( ! is_search() ) {
		return;
	}

	// We are already at the right search result page.
	if ( is_shop() || is_tax( get_object_taxonomies( 'product' ) ) ) {
		return;
	}

	$search_query = get_search_query();
	$shop_url     = wc_get_page_permalink( 'shop' );
	$redirect_url = add_query_arg( 's', rawurlencode( $search_query ), $shop_url );
	wp_safe_redirect( $redirect_url );
	exit();
}

add_action( 'template_redirect', 'product_search_only_redirect_search_to_products' );

/**
 * Clears the 's' parameter from the query if the search term is empty in the request.
 *
 * @param WP $wp The WordPress environment object containing query variables.
 *
 * @return void
 */
function product_search_only_clear_empty_search_from_request( $wp ) {
	if ( isset( $_GET['s'] ) && empty( trim( $_GET['s'] ) ) ) { // phpcs:ignore WordPress.Security
		unset( $wp->query_vars['s'] );
	}
}

add_action( 'parse_request', 'product_search_only_clear_empty_search_from_request' );

/**
 * Do not redirect to the single product page if only one product was found in the search.
 */
add_filter( 'woocommerce_redirect_single_search_result', '__return_false' );