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/app/admin/events/[id]/page.tsx

@@ -84,7 +84,7 @@ export default function AdminEventDetailPage() {
   const [showNoteModal, setShowNoteModal] = useState(false);
   const [selectedTicket, setSelectedTicket] = useState<Ticket | null>(null);
   const [noteText, setNoteText] = useState('');
-  // Unified Add Ticket modal (paid / unpaid / guest via segmented control)
+  // Unified Add Ticket modal (paid / door / unpaid / guest via segmented control)
   const [showAddTicketModal, setShowAddTicketModal] = useState(false);
   const [addTicketForm, setAddTicketForm] = useState<AddTicketFormState>(EMPTY_ADD_TICKET_FORM);
   const [submitting, setSubmitting] = useState(false);
@@ -222,7 +222,7 @@ export default function AdminEventDetailPage() {
       const res = await ticketsApi.adminAdd({
         eventId: event.id,
         type: addTicketForm.type,
-        firstName: addTicketForm.firstName,
+        firstName: addTicketForm.firstName || undefined,
         lastName: addTicketForm.lastName || undefined,
         email: addTicketForm.email || undefined,
         phone: addTicketForm.phone || undefined,