In a way the deploy playbook can be completely separate from the provisioning playbooks. The only thing the deploy playbook requires is a parent directory with permissions to create folders/files.
Our server.yml playbook creates /srv/www/site_name with the proper permissions and then the deploy.yml playbook takes over from there creating the proper directory structure within that and closing the repo + setting symlinks.
So in your case you can just set the web_user variable to deploy. There’s probably going to be some other variables to customize like the normal wordpress_sites and the paths. Your Nginx/Apache config including SSL is separate and wouldn’t be affected by this.
Also remember your virtual host web root would need to point to the deploy location including current/.