No sign-in. POST /api/v1/chat/guest/stream — a dedicated route
(Goal 1a), separate from the signed-in /chat/stream. Identity is a
guest_id httpOnly cookie minted on your first message; the backend
resolves history and the message cap from it server-side, so this page no longer
tracks the conversation itself — reloading keeps your history and your remaining
quota. Tier is forced to lite. Rate limited to 10 requests/minute,
and capped at a small number of messages for good — once hit,
sign in to keep chatting.