Does it use http or MQTT?

Home Assistant uses HTTP for this. Realistically, you won’t see much difference between HTTP and MQTT for this use case.

MQTT is harder to secure than HTTP, and has some limitations (eg it normally only supports username and password auth - no SSO, no 2FA) so I’d avoid it for anything public-facing unless you have a specific reason to use it. Using it via a VPN is fine, but you’d still need to configure a separate MQTT username and password per user.