TL;DR

Open `about:config`

Set `browser.ml.chat.hideLocalhost` to `false`

Chatbot sidebar shows "localhost" when Open WebUI runs there.

Change `browser.ml.chat.provider` to the correct URL.

Despite the common plan for many browsers to include their own local model, I feel nobody is really promoting a practical workflow for in-browser LLM side-usage. It's a good time to explore designs like this.