Zero-dependency, zero-backend HTML chat UI for the LiteLLM gateway. The
browser talks straight to :4000 (gateway CORS is open), so it's just one
file you open — no container, no stack. System-prompt textarea, model
datalist, streaming SSE, renders reasoning_content for the -thinking/
-reasoning models, settings persist in localStorage.
Deliberately never sends a `tools` field, sidestepping the vLLM "tools
must not be an empty array" bug that breaks the LiteLLM admin UI
playground for vLLM-backed models (litellm #6228; the gateway's
strip_empty_tools hook can't reach the UI's in-process completion call).
Verified against the live gateway: streams + parses a real completion
with no tools sent.
