feat(backend): FastAPI + libSQL + auth register/login/me + tests (TDD)

- FastAPI app with lifespan, CORS, health endpoint
- SQLAlchemy 2.0 async with aiosqlite, Base/UUIDMixin/TenantMixin/TimestampMixin
- Tenant and User models with multi-tenant isolation
- Auth: register (creates tenant+user), login, /me endpoint
- JWT HS256 tokens, bcrypt password hashing
- Alembic async setup with initial migration
- 6 passing tests (register, login, wrong password, me, no token, health)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/app/main.py

@@ -0,0 +1,35 @@
+from contextlib import asynccontextmanager
+
+from fastapi import FastAPI
+from fastapi.middleware.cors import CORSMiddleware
+
+from app.auth.router import router as auth_router
+from app.config import settings
+from app.db.base import Base
+from app.db.session import engine
+
+# Import models so Base.metadata knows about them
+import app.db.models  # noqa: F401
+
+
+@asynccontextmanager
+async def lifespan(app: FastAPI):
+    async with engine.begin() as conn:
+        await conn.run_sync(Base.metadata.create_all)
+    yield
+
+
+app = FastAPI(lifespan=lifespan)
+app.add_middleware(
+    CORSMiddleware,
+    allow_origins=settings.CORS_ORIGINS.split(","),
+    allow_methods=["*"],
+    allow_headers=["*"],
+    allow_credentials=True,
+)
+app.include_router(auth_router, prefix="/api/auth")
+
+
+@app.get("/api/health")
+async def health():
+    return {"status": "ok"}