refactor: standardize modular architecture patterns

- Rename module definition variables to follow naming convention:
  - catalog/definition.py: module → catalog_module
  - checkout/definition.py: module → checkout_module
  - cart/definition.py: module → cart_module

- Add router attachment functions for lazy loading:
  - get_catalog_module_with_routers()
  - get_checkout_module_with_routers()
  - get_cart_module_with_routers()

- Move billing exceptions to exceptions.py:
  - Add backwards-compatible aliases (BillingServiceError, etc.)
  - Update billing_service.py to import from exceptions.py

- Standardize VendorEmailSettingsService DI pattern:
  - Change from db in __init__ to db as method parameter
  - Create singleton vendor_email_settings_service instance
  - Update routes and tests to use new pattern

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

app/modules/catalog/definition.py

@@ -9,7 +9,28 @@ from app.modules.base import (
 )
 from app.modules.enums import FrontendType
 
-module = ModuleDefinition(
+
+# =============================================================================
+# Router Lazy Imports
+# =============================================================================
+
+
+def _get_admin_router():
+    """Lazy import of admin router to avoid circular imports."""
+    from app.modules.catalog.routes.api.admin import admin_router
+
+    return admin_router
+
+
+def _get_vendor_router():
+    """Lazy import of vendor router to avoid circular imports."""
+    from app.modules.catalog.routes.api.vendor import vendor_router
+
+    return vendor_router
+
+
+# Catalog module definition
+catalog_module = ModuleDefinition(
     code="catalog",
     name="Product Catalog",
     description="Product catalog browsing and search for storefronts",
@@ -85,3 +106,18 @@ module = ModuleDefinition(
         ],
     },
 )
+
+
+def get_catalog_module_with_routers() -> ModuleDefinition:
+    """
+    Get catalog module with routers attached.
+
+    This function attaches the routers lazily to avoid circular imports
+    during module initialization.
+    """
+    catalog_module.admin_router = _get_admin_router()
+    catalog_module.vendor_router = _get_vendor_router()
+    return catalog_module
+
+
+__all__ = ["catalog_module", "get_catalog_module_with_routers"]