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/README.md

@@ -15,7 +15,7 @@ pytest tests/integration/api/v1/ -v
 # Run specific area
 pytest tests/integration/api/v1/vendor/ -v
 pytest tests/integration/api/v1/admin/ -v
-pytest tests/integration/api/v1/public/ -v
+pytest tests/integration/api/v1/platform/ -v
 pytest tests/integration/api/v1/shared/ -v
 ```