You should install it, because it's exactly what you just described.
Edit: From a UI perspective, it's exactly what you described. There's a dropdown where you select the LLM, and there's a ChatGPT-style chatbox. You just docker-up and go to town.
Maybe I don't understand the rest of the request, but I can't imagine a software where a webpage exists and it just magically has LLMs available in the browser with no installation?