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/storefront-api-reference.md

@@ -814,8 +814,8 @@ X-RateLimit-Reset: 1700000000
 **Old Pattern (Deprecated):**
 
 ```http
-GET /api/v1/public/vendors/{vendor_id}/products
-POST /api/v1/public/vendors/auth/{vendor_id}/customers/login
+GET /api/v1/platform/vendors/{vendor_id}/products
+POST /api/v1/platform/vendors/auth/{vendor_id}/customers/login
 ```
 
 **New Pattern (Current):**