Build a Matagi-branded, single-user "Agentic Gmail" — a chat app that is a fully agentic control plane for a Gmail account. The user types in plain language; an LLM agent loop runs real Gmail actions (search, count, read, triage, label, archive, trash, draft, send, reply) rendered as live, branded Gmail tool cards. Use when someone wants to build, extend, restyle, or redeploy this app, or any Matagi internal tool that drives a connected app through a chat agent. Covers the design system, the auth model, the runtime wiring (Vercel + connection proxy + LLM completion), the JSON tool-calling loop, the Gmail tool registry, optional conversation history + a past-chats sidebar (Supabase), and deployment.
