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>

docs/deployment/stripe-integration.md

@@ -472,7 +472,7 @@ async def setup_payments(
     }
 
 
-# app/api/v1/public/vendors/payments.py
+# app/api/v1/platform/vendors/payments.py
 @router.post("/{vendor_id}/payments/create-intent")
 async def create_payment_intent(
     vendor_id: int,
@@ -535,7 +535,7 @@ class CheckoutManager {
 
     async initializePayment(orderData) {
         // Create payment intent
-        const response = await fetch(`/api/v1/public/vendors/${this.vendorId}/payments/create-intent`, {
+        const response = await fetch(`/api/v1/platform/vendors/${this.vendorId}/payments/create-intent`, {
             method: 'POST',
             headers: { 'Content-Type': 'application/json' },
             body: JSON.stringify({
@@ -585,7 +585,7 @@ Customer proceeds to checkout
     ↓
 System creates Order (payment_status: pending)
     ↓
-Frontend calls POST /api/v1/public/vendors/{vendor_id}/payments/create-intent
+Frontend calls POST /api/v1/platform/vendors/{vendor_id}/payments/create-intent
     ↓
 PaymentService creates Stripe PaymentIntent with vendor destination
     ↓