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>

docs/proposals/plan-perms.md

@@ -650,4 +650,3 @@ ADD COLUMN is_custom BOOLEAN DEFAULT FALSE;
 4. **Soft validation** - Invalid permissions in existing roles are not automatically removed (audit trail)
 
 5. **Backward compatible** - Existing roles without `source_template_id` continue to work
-cl