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/cart/definition.py

@@ -9,7 +9,20 @@ It is session-based and does not require customer authentication.
 from app.modules.base import ModuleDefinition, PermissionDefinition
 
 
-module = ModuleDefinition(
+# =============================================================================
+# Router Lazy Imports
+# =============================================================================
+
+
+def _get_storefront_router():
+    """Lazy import of storefront router to avoid circular imports."""
+    from app.modules.cart.routes.api.storefront import router
+
+    return router
+
+
+# Cart module definition
+cart_module = ModuleDefinition(
     code="cart",
     name="Shopping Cart",
     description="Session-based shopping cart for storefronts",
@@ -42,3 +55,17 @@ module = ModuleDefinition(
     # Cart is storefront-only - no admin/vendor menus needed
     menu_items={},
 )
+
+
+def get_cart_module_with_routers() -> ModuleDefinition:
+    """
+    Get cart module with routers attached.
+
+    This function attaches the routers lazily to avoid circular imports
+    during module initialization.
+    """
+    cart_module.storefront_router = _get_storefront_router()
+    return cart_module
+
+
+__all__ = ["cart_module", "get_cart_module_with_routers"]