Managed where it counts: PHP, TLS, deploys
If “managed” means someone patches WordPress plugins for you, that is not this page. If it means you are not SSH-ing into php-fpm, it is.
Managed infrastructure
Certificates renew. The PHP runtime stays on a current 8.4. Releases are atomic enough that a bad zip does not have to stay live.
Unmanaged on purpose
Theme and plugin updates remain yours. That is WordPress’s model; wrapping it in a fake app store does not make it safer.
Questions
Do you take backups of wp-content and the database?
Deploy history keeps previous file releases. That is not a scheduled full-site WordPress backup. Keep an independent backup plugin or process for content.