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>

app/modules/billing/routes/api/platform.py

@@ -1,11 +1,11 @@
-# app/modules/billing/routes/api/public.py
+# app/modules/billing/routes/api/platform.py
 """
-Public pricing API endpoints.
+Platform pricing API endpoints.
 
 Provides subscription tier and add-on product information
 for the marketing homepage and signup flow.
 
-All endpoints are public (no authentication required).
+All endpoints are unauthenticated (no authentication required).
 """
 
 from fastapi import APIRouter, Depends