Can I show product categories in the search results before the product results?

Hello,

Well, such feature is not supported by default. But you can try to use following code snippet:

class AWS_Add_Tax {
    public $loop_start_triggered = array();
    public $current_tax = false;
    public $tax_id = 0;
    public $tax = array();
    public $tax_count = 0;
    public function __construct() {
        add_action( 'woocommerce_shop_loop', array( $this, 'woocommerce_shop_loop' ) );
        add_action( 'woocommerce_before_shop_loop_item', array( $this, 'woocommerce_shop_loop' ) );
        add_filter( 'aws_search_page_results', array( $this, 'aws_search_page_results' ), 10, 3 );
        add_filter( 'woocommerce_loop_product_link', array( $this, 'woocommerce_loop_product_link' ), 9999999 );
        add_filter( 'the_permalink', array( $this, 'woocommerce_loop_product_link' ), 9999999 );
        add_filter( 'post_link', array( $this, 'woocommerce_loop_product_link' ), 9999999 );
        add_filter( 'post_type_link', array( $this, 'woocommerce_loop_product_link' ), 9999999 );
        add_filter( 'woocommerce_product_get_image', array( $this, 'woocommerce_product_get_image' ), 10, 4 );
        add_filter( 'woocommerce_placeholder_img_src', array( $this, 'woocommerce_placeholder_img_src' )  );
        add_filter( 'wp_get_attachment_image_src', array( $this, 'wp_get_attachment_image_src' ), 99999 );
        add_filter( 'woocommerce_loop_add_to_cart_link', array( $this, 'woocommerce_loop_add_to_cart_link' ), 10, 2 );
        add_filter( 'woocommerce_sale_flash', array( $this, 'woocommerce_sale_flash' ), 10, 3 );
        add_filter( 'woocommerce_get_price_html', array( $this, 'woocommerce_get_price_html' ), 10, 2 );
        add_filter( 'posts_request', array( $this, 'filter_posts_request' ), 99999, 2 );
    }
    function woocommerce_shop_loop() {
        global $product, $post;
        if ( $product ) {
            $id = $product->get_id();
            if ( $this->current_tax && isset( $this->loop_start_triggered[$id] ) ) {
                return;
            }
            $this->current_tax = false;
            if ( isset( $_REQUEST['type_aws'] ) && isset( $this->tax[$id] ) ) {
                foreach( $this->tax[$id] as $key => $tax_term ) {
                    $this->current_tax = $tax_term;
                    unset( $this->tax[$id][$key] );
                    $this->loop_start_triggered[$id] = true;
                    break;
                }
            }
        }
    }
    public function aws_search_page_results( $posts, $query, $data ) {
        $new_posts = array();
        $product = get_posts( array(
            'posts_per_page' => 1,
            'numberposts' => 1,
            'fields' => 'ids',
            'post_type' => 'product',
            'post_status' => 'publish',
            'ignore_sticky_posts' => true,
            'suppress_filters' => true,
            'no_found_rows' => 1,
            'orderby' => 'ID',
            'order' => 'ASC',
            'lang' => ''
        ) );
        foreach ( $data['search_res'] as $search_res_fields ) {
            if ( isset( $search_res_fields['tax'] ) ) {
                foreach ( $search_res_fields['tax'] as $tax_name => $tax_terms ) {
                    $this->tax_id = $product[0];
                    foreach ( $tax_terms as $tax_term ) {
                        $post = new stdClass();
                        $post->ID = $product[0];
                        $post->site_id = get_current_blog_id();
                        $post->post_name = $tax_term['name'];
                        $post->post_title = $tax_term['name'];
                        $post->permalink = $tax_term['link'];
                        $post->post_type = "product";
                        $post->post_author = "1";
                        $post->post_status = "publish";
                        $post->post_parent = 0;
                        $post->post_content = "";
                        $post->menu_order = 0;
                        $post->post_date = "2000-01-01 12:00:00";
                        $post->post_date_gmt = "2000-01-01 12:00:00";
                        $post->post_modified = "2000-01-01 12:00:00";
                        $post->post_modified_gmt = "2000-01-01 12:00:00";
                        $post->awssearch = true;
                        $post->aws_tax = true;
                        $post->aws_img = $tax_term['image'];
                        if ( $post ) {
                            $new_posts[] = $post;
                        }
                        $this->tax[$post->ID][] = $tax_term;
                    }
                }
            }
        }
        if ( ! empty( $new_posts ) ) { 
            $posts = array_merge($new_posts, $posts);
        }
        $this->tax_count = count( $posts );
        return $posts;
    }
    public function woocommerce_loop_product_link( $link ) {
        global $post;
        if ( $post && property_exists( $post, 'aws_tax' ) && $post->aws_tax ) {
            return $post->permalink;
        }
        if ( $this->current_tax && isset( $this->current_tax['link'] ) ) {
            return $this->current_tax['link'];
        }
        return $link;
    }
    public function woocommerce_product_get_image( $image, $product, $size, $attr ) {
        global $post;
        if ( $post->aws_tax ) {
            $placeholder = wc_placeholder_img_src();
            return '<img src="' . $placeholder . '"/>';
        }
        if ( $this->current_tax ) {
            if ( isset( $this->current_tax['image'] ) ) {
                return '<img src="' . esc_url( $this->current_tax['image'] ) . '"/>';;
            }
            return wc_placeholder_img( $size, $attr );
        }
        return $image;
    }
    public function woocommerce_placeholder_img_src( $src ) {
        if ( $post && property_exists( $post, 'aws_tax' ) && $post->aws_tax && $post->aws_img ) {
            return $post->aws_img;
        }
        return $src;
    }
    public function wp_get_attachment_image_src( $image ) {
        global $post;
        if ( $this->current_tax && $post && property_exists( $post, 'aws_tax' ) && $post->aws_tax && $post->aws_img ) {
            return array( $post->aws_img, '', '' );
        }
        if ( $this->current_tax && isset( $this->current_tax['id'] ) ) {
            $post_thumbnail_id = get_post_thumbnail_id( $this->current_tax['id'] );
            remove_filter( 'wp_get_attachment_image_src', array( $this, 'wp_get_attachment_image_src' ), 99999);
            $attachment_image = wp_get_attachment_image_src( $post_thumbnail_id );
            add_filter( 'wp_get_attachment_image_src', array( $this, 'wp_get_attachment_image_src' ), 99999);
            if ( $attachment_image ) {
                $image = $attachment_image;
            }
        }
        return $image;
    }
    public function woocommerce_loop_add_to_cart_link( $output, $product ) {
        $id = $product->get_id();
        if ( isset( $_REQUEST['type_aws'] ) && isset( $this->tax[$id] ) ) {
            return '';
        }
        return $output;
    }
    public function woocommerce_sale_flash( $output, $post, $product ) {
        $id = $product->get_id();
        if ( isset( $_REQUEST['type_aws'] ) && isset( $this->tax[$id] ) ) {
            return '';
        }
        return $output;
    }
    public function woocommerce_get_price_html( $output, $product ) {
        $id = $product->get_id();
        if ( isset( $_REQUEST['type_aws'] ) && isset( $this->tax[$id] ) ) {
            return '';
        }
        return $output;
    }
    public function filter_posts_request( $request, $query ) {
        $query->found_posts = $this->tax_count;
        return $request;
    }
}
new AWS_Add_Tax();

You need to add it somewhere outside the plugins folder. For example, inside functions.php file of your theme or use some plugin for adding code snippets.

Regards