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>

docs/api/authentication.md

@@ -229,12 +229,12 @@ In path-based development mode, the full URL includes the vendor code (e.g., `/v
 
 **Login Endpoint:**
 ```
-POST /api/v1/public/vendors/{vendor_id}/customers/login
+POST /api/v1/platform/vendors/{vendor_id}/customers/login
 ```
 
 **Example Request:**
 ```bash
-curl -X POST http://localhost:8000/api/v1/public/vendors/1/customers/login \
+curl -X POST http://localhost:8000/api/v1/platform/vendors/1/customers/login \
   -H "Content-Type: application/json" \
   -d '{"username":"customer","password":"customer123"}'
 ```
@@ -950,7 +950,7 @@ curl http://localhost:8000/api/v1/admin/vendors \
 
 ```bash
 # Login
-curl -X POST http://localhost:8000/api/v1/public/vendors/1/customers/login \
+curl -X POST http://localhost:8000/api/v1/platform/vendors/1/customers/login \
   -H "Content-Type: application/json" \
   -d '{"username":"customer","password":"customer123"}'