Add modernized Payment Intents pattern with Payment Element

- Restore Payment Intents flow removed by PR, updated for modern best practices
- Use Payment Element instead of legacy Card Element
- Use stripe.confirmPayment() instead of deprecated confirmCardPayment()
- Use automatic_payment_methods instead of hardcoded payment_method_types
- Split Python/JS into separate fenced code blocks for clarity
- Add guidance on when to use Payment Intents vs Checkout Sessions
- Renumber subsequent patterns (Subscription → 4, Customer Portal → 5)

plugins/payment-processing/skills/stripe-integration/SKILL.md

@@ -26,7 +26,7 @@ Master Stripe payment processing integration for robust, PCI-compliant payment f
 - Recommended for most integrations
 - Supports all UI paths:
   - Stripe-hosted checkout page
-  - Embedded checkout form
+  - Embedded checkout form (`ui_mode='embedded'`)
   - Custom UI with Elements (Payment Element, Express Checkout Element) using `ui_mode='custom'`
 - Provides built-in checkout capabilities (line items, discounts, tax, shipping, address collection, saved payment methods, and checkout lifecycle events)
 - Lower integration and maintenance burden than Payment Intents
@@ -79,7 +79,6 @@ stripe.api_key = "sk_test_..."
 
 # Create a checkout session
 session = stripe.checkout.Session.create(
-    payment_method_types=['card'],
     line_items=[{
         'price_data': {
             'currency': 'usd',
@@ -155,19 +154,19 @@ def create_checkout_session_for_elements(amount, currency='usd'):
         }],
         return_url='https://yourdomain.com/complete?session_id={CHECKOUT_SESSION_ID}'
     )
-    return session.client_secret  # Send to frontend
+    return session.client_secret  # Send to frontend for stripe.initCheckout()
 
 # Frontend (JavaScript)
 """
 const stripe = Stripe('pk_test_...');
-const appearance = { theme: 'stripe' };
 
+// initCheckout() is synchronous; loadActions() is async
 const checkout = stripe.initCheckout({clientSecret});
 const loadActionsResult = await checkout.loadActions();
 
 if (loadActionsResult.type === 'success') {
-    const session = loadActionsResult.actions.getSession();
     const {actions} = loadActionsResult;
+    const session = actions.getSession();
 
     const button = document.getElementById('pay-button');
     const checkoutContainer = document.getElementById('checkout-container');
@@ -175,7 +174,7 @@ if (loadActionsResult.type === 'success') {
     const emailErrors = document.getElementById('email-errors');
     const errors = document.getElementById('confirm-errors');
 
-    // Display total to user
+    // Display grand total (amount in smallest currency unit, e.g. cents)
     checkoutContainer.append(`Total: ${session.total.total.amount}`);
 
     // Mount Payment Element
@@ -199,7 +198,48 @@ if (loadActionsResult.type === 'success') {
 """
 ```
 
-### Pattern 3: Subscription Creation
+### Pattern 3: Payment Intents with Payment Element (Bespoke Control)
+
+Use this when you need full control over the payment flow and cannot use Checkout Sessions
+(e.g., you have your own tax, discount, or subscription calculation engine).
+
+```python
+def create_payment_intent(amount, currency='usd', customer_id=None):
+    """Create a payment intent for bespoke checkout UI with Payment Element."""
+    intent = stripe.PaymentIntent.create(
+        amount=amount,
+        currency=currency,
+        customer=customer_id,
+        automatic_payment_methods={
+            'enabled': True,
+        },
+    )
+    return intent.client_secret  # Send to frontend
+```
+
+```javascript
+// Frontend: Mount Payment Element and confirm via Payment Intents
+const stripe = Stripe('pk_test_...');
+const elements = stripe.elements({clientSecret});
+
+const paymentElement = elements.create('payment');
+paymentElement.mount('#payment-element');
+
+document.getElementById('pay-button').addEventListener('click', async () => {
+    const {error} = await stripe.confirmPayment({
+        elements,
+        confirmParams: {
+            return_url: 'https://yourdomain.com/complete',
+        },
+    });
+
+    if (error) {
+        document.getElementById('errors').textContent = error.message;
+    }
+});
+```
+
+### Pattern 4: Subscription Creation
 
 ```python
 def create_subscription(customer_id, price_id):
@@ -222,7 +262,7 @@ def create_subscription(customer_id, price_id):
         raise
 ```
 
-### Pattern 4: Customer Portal
+### Pattern 5: Customer Portal
 
 ```python
 def create_customer_portal_session(customer_id):
@@ -432,7 +472,7 @@ def test_payment_flow():
         amount=1000,
         currency='usd',
         customer=customer.id,
-        payment_method_types=['card']
+        automatic_payment_methods={'enabled': True},
     )
 
     # Confirm with test card