Send the customer confirmation email from the payment webhook

The webhook route previously assumed the backend's confirm-payment
endpoint sent the customer confirmation email; the backend assumed the
opposite. Net effect: a successful Stripe payment never triggered any
confirmation email. Consume the order snapshot confirm-payment now
returns and send it from here, matching what the checkout route already
does for a manual/Überweisung order.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

app/lib/payments/confirmPaymentEmail.ts

@@ -0,0 +1,31 @@
+import { sendOrderConfirmationEmail, type OrderConfirmationEmailData } from "../orderEmail";
+import { sendCriticalAlert } from "../alertAdmin";
+
+// The `order` snapshot returned by the backend's confirm-payment endpoint
+// (see docker/payload's src/lib/endpoints/confirmPayment.ts) — matches
+// OrderConfirmationEmailData minus `customerEmail`, which is passed
+// separately to sendOrderConfirmationEmail. Backend has no SMTP-based
+// order-confirmation sender of its own (only the 4 status-change
+// templates), so it returns everything needed here instead of the
+// frontend needing an authenticated order-read path it doesn't otherwise
+// have (ORDER_SERVICE_SECRET only ever authorizes *creating* an order).
+export type ConfirmPaymentOrderSnapshot = OrderConfirmationEmailData & { customerEmail: string };
+
+// Called from both the real Stripe webhook route and its PAYMENT_TEST_MODE
+// test-confirm sibling, right after confirm-payment reports success (and
+// NOT `alreadyProcessed: true` — a repeat delivery must never resend
+// this). Mirrors exactly what app/api/checkout/route.ts already does for
+// a manual/Überweisung order today, just triggered from the payment
+// webhook instead of the checkout request itself for gated methods.
+export async function sendConfirmedPaymentEmail(order: ConfirmPaymentOrderSnapshot): Promise<void> {
+  const { customerEmail, ...emailData } = order;
+  try {
+    await sendOrderConfirmationEmail(emailData, customerEmail);
+  } catch (err) {
+    sendCriticalAlert("Bestätigungs-Mail konnte nach Zahlungsbestätigung nicht gesendet werden", {
+      orderNumber: order.orderNumber,
+      customerEmail,
+      error: String(err),
+    });
+  }
+}