feat: extract billing module with routes (Phase 3)

Create app/modules/billing/ directory structure with:
- definition.py: Module definition with features and menu items
- routes/admin.py: Admin billing routes with module access control
- routes/vendor.py: Vendor billing routes with module access control

Key changes:
- Billing module uses require_module_access("billing") dependency
- Admin router now includes billing module router instead of legacy
- Module registry imports billing_module from extracted location
- Routes have identical functionality but are now module-gated

Module structure pattern for future extractions:
  app/modules/{module}/
  ├── __init__.py
  ├── definition.py (ModuleDefinition + router getters)
  └── routes/
      ├── __init__.py
      ├── admin.py (require_module_access dependency)
      └── vendor.py (require_module_access dependency)

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

app/modules/billing/definition.py

@@ -0,0 +1,71 @@
+# app/modules/billing/definition.py
+"""
+Billing module definition.
+
+Defines the billing module including its features, menu items,
+and route configurations.
+"""
+
+from app.modules.base import ModuleDefinition
+from models.database.admin_menu_config import FrontendType
+
+
+def _get_admin_router():
+    """Lazy import of admin router to avoid circular imports."""
+    from app.modules.billing.routes.admin import admin_router
+
+    return admin_router
+
+
+def _get_vendor_router():
+    """Lazy import of vendor router to avoid circular imports."""
+    from app.modules.billing.routes.vendor import vendor_router
+
+    return vendor_router
+
+
+# Billing module definition
+billing_module = ModuleDefinition(
+    code="billing",
+    name="Billing & Subscriptions",
+    description=(
+        "Subscription tier management, vendor billing, payment processing, "
+        "and invoice history. Integrates with Stripe for payment collection."
+    ),
+    features=[
+        "subscription_management",  # Manage subscription tiers
+        "billing_history",  # View invoices and payment history
+        "stripe_integration",  # Stripe payment processing
+        "invoice_generation",  # Generate and download invoices
+        "subscription_analytics",  # Subscription stats and metrics
+        "trial_management",  # Manage vendor trial periods
+        "limit_overrides",  # Override tier limits per vendor
+    ],
+    menu_items={
+        FrontendType.ADMIN: [
+            "subscription-tiers",  # Manage tier definitions
+            "subscriptions",  # View/manage vendor subscriptions
+            "billing-history",  # View all invoices
+        ],
+        FrontendType.VENDOR: [
+            "billing",  # Vendor billing dashboard
+            "invoices",  # Vendor invoice history
+        ],
+    },
+    is_core=False,  # Billing can be disabled (e.g., internal platforms)
+)
+
+
+def get_billing_module_with_routers() -> ModuleDefinition:
+    """
+    Get billing module with routers attached.
+
+    This function attaches the routers lazily to avoid circular imports
+    during module initialization.
+    """
+    billing_module.admin_router = _get_admin_router()
+    billing_module.vendor_router = _get_vendor_router()
+    return billing_module
+
+
+__all__ = ["billing_module", "get_billing_module_with_routers"]