feat(billing): extract Billing Service (Step 4)

- stripe_service: checkout sessions, webhook handling, subscription CRUD
- tier_manager: feature matrix (4 tiers), quota enforcement, rate limits
- routes: checkout, webhook (no auth), subscription, tier query, features
- Traefik header auth (X-User-Id) replaces get_current_user dependency
- /tier/{user_id} endpoint for internal service-to-service lookups
- /features and /features/{tier} for feature matrix queries
- Dockerfile: single worker, 30s timeout (lightweight service)

services/billing/app/main.py

@@ -0,0 +1,46 @@
+"""Billing Service — FastAPI application.
+
+Owns: Stripe checkout/webhook, subscription management, tier feature matrix,
+quota enforcement.
+
+Downstream services query this service (or read the user's tier from
+the X-User-Tier header injected by Traefik) for billing decisions.
+The webhook endpoint is exposed WITHOUT ForwardAuth so Stripe can reach it.
+"""
+
+from __future__ import annotations
+
+import logging
+from contextlib import asynccontextmanager
+from typing import AsyncGenerator
+
+from fastapi import FastAPI
+from fastapi.middleware.cors import CORSMiddleware
+
+from app.routes import router
+
+logger = logging.getLogger(__name__)
+
+
+@asynccontextmanager
+async def lifespan(app: FastAPI) -> AsyncGenerator[None, None]:
+    logger.info("billing: service started")
+    yield
+    logger.info("billing: service stopped")
+
+
+app = FastAPI(title="Adiuva Billing Service", lifespan=lifespan)
+
+app.add_middleware(
+    CORSMiddleware,
+    allow_origins=["*"],
+    allow_methods=["GET", "POST", "DELETE"],
+    allow_headers=["*"],
+)
+
+app.include_router(router)
+
+
+@app.get("/health")
+async def health() -> dict[str, str]:
+    return {"status": "ok", "service": "billing"}