If you want the top search (on red background) to search in the Adverts instead of posts you would need to customize the search form and make sure that:
1. form “action” param is set to the page with [adverts_list] shortcode.
2. the text input name is “query”.
How to do that i am not really sure, as this search form is part of the theme (i think) it would be best to ask the theme author about it.
One workaround you can try is to add the code below in your theme functions.php it should redirect the searches in the top bar to your page with [adverts_list] shortcode.
add_action( "wp", function() {
if( isset( $_GET["s"] ) && ! empty( $_GET["s"] ) ) {
$url = get_permalink( adverts_config( "ads_list_id" ) );
$url = add_query_arg( "query", $_GET["s"], $url );
wp_redirect( $url );
}
});