How to find a post id using the post_excerpt?

You can get the post ID from the excerpt, but as far as I can tell, WP_Query doesn’t support this (very well), so you need to write a custom WPDB query.

function get_post_id_by_excerpt($excerpt) {
    global $wpdb;
    $result = $wpdb->get_row( 
        $wpdb->prepare("SELECT ID FROM {$wpdb->prefix}posts WHERE post_excerpt LIKE %s", $excerpt) 
    );
    return $result;
}

For this to work, you need to pass the exact excerpt (incl. HTML) to the function