Can I vibecode MagicChat?

Build me an AI support chatbot that trains on my own website and docs, to replace
MagicChat, in an empty repo.

Stack (no alternatives): Next.js 15 (App Router) + TypeScript, Postgres with the
pgvector extension via Drizzle ORM, and Docker Compose so `docker compose up` runs
Postgres and the app together. Use the OpenAI or Anthropic API for both embeddings
and answers (keys in .env).

Core loop:
- `npm run ingest -- <sitemap-or-url>`: crawl the pages, strip to clean text, chunk
  (~800 tokens with overlap), embed each chunk, and store text + vector + source URL
  in Postgres.
- A /api/chat route: embed the incoming question, pull the top-k chunks by cosine
  similarity, and ask the LLM to answer ONLY from that context, returning the source
  URLs it used. Stream the answer.
- A single embeddable widget: one <script> tag mounts a floating chat bubble on any
  site, talking to /api/chat with CORS locked to configured origins.

Details:
- One config file: bot name, greeting, allowed origins, model, top-k.
- Store everything locally in Postgres; `npm run reindex` re-crawls and replaces.
- Secrets in .env, ship .env.example, never commit keys.
- Handle empty, loading, and "I don't know from the docs" states honestly; never
  invent answers outside the retrieved context.
- Out of scope: multi-channel (email/WhatsApp/Slack), team seats, an analytics
  dashboard, human handoff, scheduled auto-refresh (leave a documented cron hook),
  and any hosted control plane.
- README: setup, the ingest command, embedding the widget, and where data lives.