Centralize seat capacity accounting and the payment provider registry.

Replace manualProviders.ts with a paymentProviders.ts registry
(automatic vs manual settlement) and move all seat counting into
capacity.ts as the single source of truth: only paid/checked-in tickets
and pending_approval payments hold a seat, so abandoned checkouts never
block sales. Admins can now knowingly approve a payment over capacity
(allowOverCapacity), with the booking and admin UIs updated to match.

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

frontend/src/lib/api/client.ts

@@ -34,7 +34,12 @@ export async function fetchApi<T>(
     const errorMessage = typeof errorData.error === 'string'
       ? errorData.error
       : (errorData.message || JSON.stringify(errorData) || 'Request failed');
-    throw new Error(errorMessage);
+    const error = new Error(errorMessage);
+    // Preserve structured error info (e.g. code: 'EVENT_OVER_CAPACITY') so
+    // callers can react beyond the message text.
+    (error as any).code = errorData.code;
+    (error as any).data = errorData;
+    throw error;
   }
 
   return res.json();