Review this post, which outlines how to commission a Matter device using the Python Matter Server admin dashboard instead of HA. If you are trying to do this programmatically, review the documentation for the Python Matter Server websockets API that HA is using for underlying communication.
You can review the developer documentation for the REST APi and websockets API for what can be done outside the HA interface. Whether you’re using HAOS is not relevant, as all versions have access to the same external APIs.