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>

tests/integration/api/v1/platform/README.md

@@ -1,4 +1,4 @@
-# Public API Integration Tests
+# Platform API Integration Tests
 
 ## Documentation
 
@@ -9,8 +9,8 @@ For comprehensive testing documentation, see:
 ## Quick Start
 
 ```bash
-# Run all public tests
-pytest tests/integration/api/v1/public/ -v
+# Run all platform tests
+pytest tests/integration/api/v1/platform/ -v
 ```
 
 ## Status