refactor: rename public routes and templates to platform

Complete the public -> platform naming migration across the codebase.
This aligns with the naming convention where "platform" refers to
the marketing/public-facing pages of the platform itself.

Changes:
- Update all imports from public to platform modules
- Update template references from public/ to platform/
- Update route registrations to use platform prefix
- Update documentation to reflect new naming
- Update test files for platform API endpoints

Files affected:
- app/api/main.py - router imports
- app/modules/*/routes/*/platform.py - route definitions
- app/modules/*/templates/*/platform/ - template files
- app/modules/routes.py - route discovery
- docs/* - documentation updates
- tests/integration/api/v1/platform/ - test files

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

scripts/test_auth_complete.py

@@ -273,7 +273,7 @@ def test_customer_login() -> dict | None:
 
     try:
         response = requests.post(
-            f"{BASE_URL}/api/v1/public/vendors/1/customers/login",
+            f"{BASE_URL}/api/v1/platform/vendors/1/customers/login",
             json={"username": "customer", "password": "customer123"},
         )