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/app/admin/events/page.tsx

@@ -222,7 +222,14 @@ export default function AdminEventsPage() {
                       </div>
                     </td>
                     <td className="px-4 py-3 text-sm text-gray-600">{formatDate(event.startDatetime)}</td>
-                    <td className="px-4 py-3 text-sm">{event.bookedCount || 0} / {event.capacity}</td>
+                    <td className="px-4 py-3 text-sm">
+                      {(event.bookedCount || 0) + (event.claimedCount || 0)} / {event.capacity}
+                      {(event.claimedCount || 0) > 0 && (
+                        <span className="block text-[11px] text-yellow-600">
+                          {event.claimedCount} pending approval
+                        </span>
+                      )}
+                    </td>
                     <td className="px-4 py-3">
                       <div className="flex items-center gap-1.5">
                         {getStatusBadge(event.status)}
@@ -332,7 +339,12 @@ export default function AdminEventsPage() {
                     </div>
                   </div>
                   <div className="flex items-center justify-between mt-2 pt-2 border-t border-gray-100">
-                    <p className="text-xs text-gray-500">{event.bookedCount || 0} / {event.capacity} spots</p>
+                    <p className="text-xs text-gray-500">
+                      {(event.bookedCount || 0) + (event.claimedCount || 0)} / {event.capacity} spots
+                      {(event.claimedCount || 0) > 0 && (
+                        <span className="text-yellow-600"> · {event.claimedCount} pending</span>
+                      )}
+                    </p>
                     <div className="flex items-center gap-1" onClick={(e) => e.stopPropagation()}>
                       <Link href={`/admin/events/${event.id}`}
                         className="p-2 hover:bg-primary-yellow/20 text-primary-dark rounded-btn min-h-[36px] min-w-[36px] flex items-center justify-center">