Add "paid at the door" ticket type to the Add Ticket modal.

Door walk-ins were only expressible as an unpaid ticket, which left the
cash out of revenue. The new type records the cash payment as paid and
makes every field optional, since a walk-in often gives no details:
a blank name is logged as "Walk-in", and a confirmation email only goes
out when an email is entered.

Door tickets reuse paymentStatus 'paid' (the column enum is capped at
paid/unpaid/comp) so badges and revenue totals pick them up with no
migration; the cash payment row is referenced "Paid at door" to keep
them distinguishable from emailed manual tickets.

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

frontend/src/lib/api/tickets.ts

@@ -106,11 +106,12 @@ export const ticketsApi = {
     }),
 
   // Unified add-attendee endpoint behind the single Add Ticket modal
-  // (paid = confirmation + QR, unpaid = pay link + door collection, guest = free comp)
+  // (paid = confirmation + QR, door = cash taken at the door, unpaid = pay link +
+  // door collection, guest = free comp)
   adminAdd: (data: {
     eventId: string;
-    type: 'paid' | 'unpaid' | 'guest';
-    firstName: string;
+    type: 'paid' | 'door' | 'unpaid' | 'guest';
+    firstName?: string;
     lastName?: string;
     email?: string;
     phone?: string;