Add Stripe subscription billing integration

- Add stripe_customer_id and stripe_subscription_id fields to User model
- Add Stripe config settings (secret key, publishable key, price ID, webhook secret)
- Create billing API endpoints: checkout session, webhook handler, portal, status
- Add frontend Billing page with upgrade/manage subscription UI
- Add billing route and Pro nav link
- Add stripe dependency to requirements

backend/app/core/config.py

@@ -22,6 +22,12 @@ class Settings(BaseSettings):
     # Claude API
     ANTHROPIC_API_KEY: str = ""
 
+    # Stripe
+    STRIPE_SECRET_KEY: str = ""
+    STRIPE_PUBLISHABLE_KEY: str = ""
+    STRIPE_PRICE_ID: str = ""
+    STRIPE_WEBHOOK_SECRET: str = ""
+
     # Frontend
     FRONTEND_URL: str = "http://localhost:5173"