feat(01-01): Backend FastAPI skeleton + Docker build config

- FastAPI app with SPAStaticFiles catch-all (root_path NOT in constructor)
- config.py with DATA_PATH, PROMPTS_PATH, OUTPUTS_PATH, CAMPAIGNS_PATH, CONFIG_PATH
- Startup lifespan creates data directories automatically
- Health endpoint: GET /api/health -> {"status": "ok"}
- Dockerfile multi-stage: node:22-slim builds React, python:3.12-slim serves API+SPA
- --root-path /postgenerator set in Uvicorn CMD only (avoids Pitfall #4)
- docker-compose.yml: lab-postgenerator-app, proxy_net, named volume for data persistence
- requirements.txt with pinned versions: fastapi[standard]==0.135.1, anthropic==0.84.0

backend/main.py

@@ -0,0 +1,78 @@
+"""PostGenerator FastAPI application.
+
+IMPORTANT: root_path is intentionally NOT set in the FastAPI() constructor.
+It is passed only via Uvicorn's --root-path flag at runtime to avoid the
+double-path bug (Pitfall #4).
+"""
+
+from contextlib import asynccontextmanager
+from pathlib import Path
+
+from fastapi import FastAPI
+from fastapi.responses import FileResponse
+from fastapi.staticfiles import StaticFiles
+
+from backend.config import CAMPAIGNS_PATH, CONFIG_PATH, OUTPUTS_PATH, PROMPTS_PATH
+
+
+# ---------------------------------------------------------------------------
+# SPA static files with catch-all fallback
+# ---------------------------------------------------------------------------
+
+class SPAStaticFiles(StaticFiles):
+    """Serve a React SPA: return index.html for any 404 so the client-side
+    router handles unknown paths instead of returning a 404 from the server."""
+
+    async def get_response(self, path: str, scope):
+        try:
+            return await super().get_response(path, scope)
+        except Exception:
+            # Fall back to index.html for client-side routing
+            return await super().get_response("index.html", scope)
+
+
+# ---------------------------------------------------------------------------
+# Startup / shutdown lifecycle
+# ---------------------------------------------------------------------------
+
+@asynccontextmanager
+async def lifespan(app: FastAPI):
+    """Create required data directories on startup if they do not exist."""
+    for directory in (PROMPTS_PATH, OUTPUTS_PATH, CAMPAIGNS_PATH, CONFIG_PATH):
+        directory.mkdir(parents=True, exist_ok=True)
+    yield
+    # Nothing to clean up on shutdown
+
+
+# ---------------------------------------------------------------------------
+# Application
+# ---------------------------------------------------------------------------
+
+# CRITICAL: Do NOT pass root_path here — use Uvicorn --root-path instead.
+app = FastAPI(
+    title="PostGenerator",
+    description="Instagram carousel post generator powered by Claude",
+    version="0.1.0",
+    lifespan=lifespan,
+    # root_path is intentionally absent — set via Uvicorn --root-path at runtime
+)
+
+
+# ---------------------------------------------------------------------------
+# API routes (must be registered BEFORE the SPA catch-all mount)
+# ---------------------------------------------------------------------------
+
+@app.get("/api/health")
+async def health() -> dict:
+    """Health check endpoint."""
+    return {"status": "ok"}
+
+
+# ---------------------------------------------------------------------------
+# SPA catch-all mount (MUST be last — catches everything not matched above)
+# ---------------------------------------------------------------------------
+
+_STATIC_DIR = Path(__file__).parent.parent / "static"
+
+if _STATIC_DIR.exists():
+    app.mount("/", SPAStaticFiles(directory=str(_STATIC_DIR), html=True), name="spa")