> Home Assistant has support for that remote option, and no others.

The openHAB Cloud Connector allows connecting the local openHAB runtime to a remote openHAB Cloud instance, such as myopenHAB.org, which is an instance of the openHAB Cloud service hosted by the openHAB Foundation (https://www.openhab.org/addons/integrations/openhabcloud/)

> There is also a container-based method that can run on another distribution, but this installation does not support the add-ons feature.

You can use the add-ons with the containerized version. This has been discussed elsewhere.