feat: implement user authentication module

- Backend (FastAPI):
  - External API authentication (pj-auth-api.vercel.app)
  - JWT token validation with Redis session storage
  - RBAC with department isolation
  - User, Role, Department models with pjctrl_ prefix
  - Alembic migrations with project-specific version table
  - Complete test coverage (13 tests)

- Frontend (React + Vite):
  - AuthContext for state management
  - Login page with error handling
  - Protected route component
  - Dashboard with user info display

- OpenSpec:
  - 7 capability specs defined
  - add-user-auth change archived

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/app/main.py

@@ -0,0 +1,32 @@
+from fastapi import FastAPI
+from fastapi.middleware.cors import CORSMiddleware
+
+from app.api.auth import router as auth_router
+from app.api.users import router as users_router
+from app.api.departments import router as departments_router
+from app.core.config import settings
+
+app = FastAPI(
+    title="Project Control API",
+    description="Cross-departmental project management system API",
+    version="0.1.0",
+)
+
+# CORS middleware
+app.add_middleware(
+    CORSMiddleware,
+    allow_origins=settings.CORS_ORIGINS,
+    allow_credentials=True,
+    allow_methods=["*"],
+    allow_headers=["*"],
+)
+
+# Include routers
+app.include_router(auth_router.router, prefix="/api/auth", tags=["Authentication"])
+app.include_router(users_router.router, prefix="/api/users", tags=["Users"])
+app.include_router(departments_router.router, prefix="/api/departments", tags=["Departments"])
+
+
+@app.get("/health")
+async def health_check():
+    return {"status": "healthy"}