Bundle FastAPI backend into Next.js Docker container

The Next.js app was proxying /api/* to the old Flask/FastAPI server
at legal-ai.nautilus.marcusgroup.org. When that server went down,
the Next.js app's API calls failed with 503.

Now both services run in the same container:
- FastAPI (uvicorn) on :8000 — the API backend
- Next.js (node) on :3000 — proxies /api/* to localhost:8000

Changes:
- Dockerfile: multi-stage build with Python 3.12 + Node.js
- next.config.ts: default proxy target is now 127.0.0.1:8000
- start.sh: launches uvicorn in background + node in foreground
- pyproject.toml: add fastapi + uvicorn as explicit deps

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

web-ui/next.config.ts

@@ -1,17 +1,14 @@
 import type { NextConfig } from "next";
 
 /**
- * Staging config — proxies /api/* and /openapi.json to the production FastAPI
- * at legal-ai.nautilus.marcusgroup.org. This lets the new Next.js UI call the
- * existing backend without CORS and without running a second FastAPI instance.
- *
- * When the rewrite branch is cut over to production, set NEXT_PUBLIC_API_BASE_URL
- * and/or move the FastAPI in front of this app via traefik routing.
+ * Proxies /api/* and /openapi.json to the FastAPI backend.
+ * In Docker both processes run in the same container, so the default
+ * target is http://127.0.0.1:8000.  Override with NEXT_PUBLIC_API_ORIGIN
+ * if the backend lives elsewhere (e.g. during local dev).
  */
 
 const API_ORIGIN =
-  process.env.NEXT_PUBLIC_API_ORIGIN ??
-  "https://legal-ai.nautilus.marcusgroup.org";
+  process.env.NEXT_PUBLIC_API_ORIGIN ?? "http://127.0.0.1:8000";
 
 const nextConfig: NextConfig = {
   output: "standalone",