GeneratePress theme compatibility/handling of WooCommerce Product Search plugin

Re: GeneratePress theme compatibility/handling of WooCommerce Product Search plugin
There's no official instructions specifically on how to set up WooCommerce Product Search plugin within Generate Press.
I'm not sure if WooCommerce Product Search plugin is compatible with Generate Press theme out of the box. Can you confirm?

I'm currently using this official GP snippet:

add_filter( 'generate_navigation_search_output', function() {
    printf(  
        '<form method="get" class="search-form navigation-search" action="%1$s">
            <input type="search" class="search-field" value="%2$s" name="s" title="%3$s" />
            <input type="hidden" name="post_type" value="product" />
        </form>', 
        esc_url( home_url( '/' ) ), 
        esc_attr( get_search_query() ),   
        esc_attr_x( 'Search', 'label', 'generatepress' ) 
    ); 
} );

And also, I'm using this GP snippet for the placeholder text:

add_filter( 'generate_navigation_search_output', function() {
    printf(
        '<form method="get" class="search-form navigation-search" action="%1$s">
            <input type="search" placeholder="Enter your search" class="search-field" value="%2$s" name="s" title="%3$s" />
        </form>',
        esc_url( home_url( '/' ) ),
        esc_attr( get_search_query() ),
        esc_attr_x( 'Search', 'label', 'generatepress' ) 
    ); 
} );

Is that correct?
Is it all that's needed?
Looking at my WooCommerce website (provided in the private notes), can you confirm if the WooCommerce Product Search plugin functionality is properly integrating with GP Theme?
Why are the search results so slow to come up?