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/marketplace/routes/pages/platform.py

@@ -1,8 +1,8 @@
-# app/modules/marketplace/routes/pages/public.py
+# app/modules/marketplace/routes/pages/platform.py
 """
-Marketplace Public Page Routes (HTML rendering).
+Marketplace Platform Page Routes (HTML rendering).
 
-Public (unauthenticated) pages:
+Platform (unauthenticated) pages:
 - Find shop (Letzshop vendor browser)
 """
 
@@ -11,7 +11,7 @@ from fastapi.responses import HTMLResponse
 from sqlalchemy.orm import Session
 
 from app.core.database import get_db
-from app.modules.core.utils.page_context import get_public_context
+from app.modules.core.utils.page_context import get_platform_context
 from app.templates_config import templates
 
 router = APIRouter()
@@ -32,10 +32,10 @@ async def find_shop_page(
 
     Allows vendors to search for and claim their Letzshop shop.
     """
-    context = get_public_context(request, db)
+    context = get_platform_context(request, db)
     context["page_title"] = "Find Your Letzshop Shop"
 
     return templates.TemplateResponse(
-        "marketplace/public/find-shop.html",
+        "marketplace/platform/find-shop.html",
         context,
     )