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/(public)/events/[id]/page.tsx

@@ -117,7 +117,10 @@ function generateEventJsonLd(event: Event) {
       '@type': 'Offer',
       price: event.price,
       priceCurrency: event.currency,
-      availability: Math.max(0, (event.capacity ?? 0) - (event.bookedCount ?? 0)) > 0
+      availability:
+        (typeof event.availableSeats === 'number'
+          ? event.availableSeats
+          : Math.max(0, (event.capacity ?? 0) - (event.bookedCount ?? 0))) > 0
         ? 'https://schema.org/InStock'
         : 'https://schema.org/SoldOut',
       url: `${siteUrl}/events/${event.slug}`,