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/routes.py

@@ -183,9 +183,9 @@ def _discover_routes_in_dir(
             "pages_prefix": "/storefront",
             "include_in_schema": True if route_type == "api" else False,
         },
-        "public": {
-            "api_prefix": "/api/v1/public",
-            "pages_prefix": "/public",
+        "platform": {
+            "api_prefix": "/api/v1/platform",
+            "pages_prefix": "/platform",
             "include_in_schema": True,
         },
         "webhooks": {
@@ -335,16 +335,16 @@ def get_storefront_api_routes() -> list[RouteInfo]:
     return sorted(routes, key=lambda r: r.priority)
 
 
-def get_public_api_routes() -> list[RouteInfo]:
+def get_platform_api_routes() -> list[RouteInfo]:
     """
-    Get public API routes from modules, sorted by priority.
+    Get platform API routes from modules, sorted by priority.
 
-    Public routes are unauthenticated endpoints for marketing pages,
+    Platform routes are unauthenticated endpoints for marketing pages,
     pricing info, and other public-facing features.
     """
     routes = [
         r for r in discover_module_routes()
-        if r.route_type == "api" and r.frontend == "public"
+        if r.route_type == "api" and r.frontend == "platform"
     ]
     return sorted(routes, key=lambda r: r.priority)
 
@@ -363,11 +363,11 @@ def get_webhooks_api_routes() -> list[RouteInfo]:
     return sorted(routes, key=lambda r: r.priority)
 
 
-def get_public_page_routes() -> list[RouteInfo]:
+def get_platform_page_routes() -> list[RouteInfo]:
     """
-    Get public (marketing) page routes from modules, sorted by priority.
+    Get platform (marketing) page routes from modules, sorted by priority.
 
-    Public pages are unauthenticated marketing pages like:
+    Platform pages are unauthenticated marketing pages like:
     - Homepage (/)
     - Pricing (/pricing)
     - Signup (/signup)
@@ -379,7 +379,7 @@ def get_public_page_routes() -> list[RouteInfo]:
     """
     routes = [
         r for r in discover_module_routes()
-        if r.route_type == "pages" and r.frontend == "public"
+        if r.route_type == "pages" and r.frontend == "platform"
     ]
     return sorted(routes, key=lambda r: r.priority)
 
@@ -414,8 +414,8 @@ __all__ = [
     "get_admin_api_routes",
     "get_vendor_api_routes",
     "get_storefront_api_routes",
-    "get_public_api_routes",
+    "get_platform_api_routes",
     "get_webhooks_api_routes",
-    "get_public_page_routes",
+    "get_platform_page_routes",
     "get_storefront_page_routes",
 ]