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/registry.py

@@ -7,11 +7,21 @@ enabled/disabled per platform. Core modules cannot be disabled.
 
 Module Granularity (Medium - ~12 modules):
 Matches menu sections for intuitive mapping between modules and UI.
+
+Module Structure:
+- Inline modules: Defined directly in this file (core, platform-admin, etc.)
+- Extracted modules: Imported from app/modules/{module}/ (billing, etc.)
+
+As modules are extracted to their own directories, they are imported
+here and their inline definitions are replaced.
 """
 
 from app.modules.base import ModuleDefinition
 from models.database.admin_menu_config import FrontendType
 
+# Import extracted modules
+from app.modules.billing.definition import billing_module
+
 
 # =============================================================================
 # Module Definitions
@@ -72,28 +82,8 @@ MODULES: dict[str, ModuleDefinition] = {
     # =========================================================================
     # Optional Modules
     # =========================================================================
-    "billing": ModuleDefinition(
-        code="billing",
-        name="Billing & Subscriptions",
-        description="Subscription tiers, billing history, and payment processing.",
-        features=[
-            "subscription_management",
-            "billing_history",
-            "stripe_integration",
-            "invoice_generation",
-        ],
-        menu_items={
-            FrontendType.ADMIN: [
-                "subscription-tiers",
-                "subscriptions",
-                "billing-history",
-            ],
-            FrontendType.VENDOR: [
-                "billing",
-                "invoices",
-            ],
-        },
-    ),
+    # Billing module - imported from app/modules/billing/
+    "billing": billing_module,
     "inventory": ModuleDefinition(
         code="inventory",
         name="Inventory Management",