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)/book/[eventId]/page.tsx

@@ -5,7 +5,7 @@ import { useParams, useRouter, useSearchParams } from 'next/navigation';
 import { useLanguage } from '@/context/LanguageContext';
 import { useAuth } from '@/context/AuthContext';
 import { eventsApi, ticketsApi, paymentOptionsApi, Event, PaymentOptionsConfig } from '@/lib/api';
-import { formatDateLong, formatTime, formatRucDisplay } from '@/lib/utils';
+import { formatDateLong, formatTime, formatRucDisplay, eventSpotsLeft, isEventSoldOut } from '@/lib/utils';
 import { isSafeExternalUrl } from '@/lib/safeRedirect';
 import toast from 'react-hot-toast';
 import type {
@@ -108,16 +108,15 @@ export default function BookingPage() {
             return;
           }
 
-          const bookedCount = eventRes.event.bookedCount ?? 0;
-          const capacity = eventRes.event.capacity ?? 0;
-          const soldOut = bookedCount >= capacity;
-          if (soldOut) {
+          // Server-authoritative availability — same formula the booking API
+          // enforces, so a sold-out event is caught here, not at submit time.
+          if (isEventSoldOut(eventRes.event)) {
             toast.error(t('events.details.soldOut'));
             router.push(`/events/${eventRes.event.slug}`);
             return;
           }
 
-          const spotsLeft = Math.max(0, capacity - bookedCount);
+          const spotsLeft = eventSpotsLeft(eventRes.event);
           setEvent(eventRes.event);
           // Cap quantity by available spots (never allow requesting more than spotsLeft)
           setTicketQuantity((q) => Math.min(q, Math.max(1, spotsLeft)));
@@ -366,6 +365,23 @@ export default function BookingPage() {
       }
     } catch (error: any) {
       toast.error(error.message || t('booking.form.errors.bookingFailed'));
+      // Capacity race on the last seats: refresh availability so the page
+      // reflects reality (sold-out block / lower quantity cap) instead of the
+      // stale counts loaded when the form was opened.
+      const message = String(error?.message || '');
+      if (/sold out|seats available/i.test(message)) {
+        try {
+          const { event: freshEvent } = await eventsApi.getById(params.eventId as string);
+          setEvent(freshEvent);
+          const freshSpots = eventSpotsLeft(freshEvent);
+          if (freshSpots > 0) {
+            setTicketQuantity((q) => Math.min(q, freshSpots));
+            setAttendees((prev) => prev.slice(0, Math.max(0, freshSpots - 1)));
+          }
+        } catch {
+          // Keep the stale event state if the refresh fails
+        }
+      }
     } finally {
       setSubmitting(false);
     }
@@ -388,8 +404,8 @@ export default function BookingPage() {
     return null;
   }
 
-  const spotsLeft = Math.max(0, event.capacity - (event.bookedCount ?? 0));
-  const isSoldOut = (event.bookedCount ?? 0) >= event.capacity;
+  const spotsLeft = eventSpotsLeft(event);
+  const isSoldOut = isEventSoldOut(event);
 
   // Paying step - waiting for Lightning payment (compact design)
   if (step === 'paying' && bookingResult && bookingResult.lightningInvoice) {