No with how I figured the architecture, it doesn’t expose the IP to anyone:
Dashboard Livestream part of the extension (the broadcaster part) uses https and tries to load a JSON file from let’s say https://127.0.0.1:12345/data.json with a simple AJAX request. This extension is loaded in the browser, which effectively means is running only when the broadcaster’s computer and only on his browser, and interacting with the webserver installed locally.
The IP is not exposed at all, since the broadcaster browser is the only one able to access the server, which doesn’t even need to open ports or anything: both things are happening locally.
After that, is all normal: broadcaster part of the extension send messages to viewer part of the extension, that’s it.