feat(260521-fci-01): add ticket reconciliation service + API route

- New lib/services/ticket-reconciliation-service.ts: reconcileStaleTickets()
  scans tickets where is_deleted=false AND status<>5 AND synced_at older than
  7 days (capped at 500), re-fetches each from Autotask, and either upserts
  via the webhook SQL pattern or soft-deletes when Autotask returns null.
- Returns { scanned, updated, statusFlippedToComplete, softDeleted, errors }.
- New POST /api/sync/reconcile-tickets — fire-and-forget trigger mirroring
  /api/sync/incremental (public per existing middleware allowlist).

app/api/sync/reconcile-tickets/route.ts

@@ -0,0 +1,31 @@
+/**
+ * Ticket Reconciliation API Endpoint
+ * POST /api/sync/reconcile-tickets - Trigger a stale-ticket reconciliation pass.
+ * Public per middleware.ts (matches /api/sync/incremental). Fire-and-forget.
+ */
+
+import { NextRequest, NextResponse } from 'next/server';
+import { reconcileStaleTickets } from '@/lib/services/ticket-reconciliation-service';
+
+export async function POST(request: NextRequest) {
+  try {
+    const body = await request.json().catch(() => ({}));
+    const triggeredBy = body.triggeredBy || 'api';
+
+    // Non-blocking — same pattern as /api/sync/incremental.
+    reconcileStaleTickets().catch((error) => {
+      console.error('[RECONCILE] Ticket reconciliation failed:', error);
+    });
+
+    return NextResponse.json({
+      message: 'Ticket reconciliation started',
+      triggeredBy,
+    });
+  } catch (error) {
+    console.error('Failed to start ticket reconciliation:', error);
+    return NextResponse.json(
+      { error: 'Failed to start ticket reconciliation' },
+      { status: 500 }
+    );
+  }
+}