Support for WebSocket Server mode?

My HA is running in the LAN, and I have no public IP address to expose HASS API. Although Hass supports websocket API, it seems that it only supports running as a server. I want Hass to directly initiate a websocket client request to connect to a server.

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What server? What API?

HA uses integrations for that, so it’s perfectly do-able if either there’s an existing Python library for that API, or the API details are available so somebody (like you) can develop one.