Fix avg resolution time using dedicated closed_at column

The dashboard's "Avg Resolution" stat was using updated_at, which gets
overwritten on any post-close edit (title change, comment, etc.),
inflating the metric. Also fixes "Closed Today" count for the same reason.

- Add closed_at TIMESTAMP column to tickets table
- Set closed_at on close, preserve on re-edit, clear on reopen
- Update StatsModel queries to use closed_at instead of updated_at
- Add migration script with audit log backfill for existing tickets

Run: php scripts/add_closed_at_column.php

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

models/TicketModel.php

@@ -216,6 +216,9 @@ class TicketModel {
      * @return array ['success' => bool, 'error' => string|null, 'conflict' => bool]
      */
     public function updateTicket(array $ticketData, ?int $updatedBy = null, ?string $expectedUpdatedAt = null): array {
+        // closed_at: set on close (preserve if already set), clear on reopen
+        $closedAtClause = "closed_at = CASE WHEN ? = 'Closed' THEN COALESCE(closed_at, NOW()) ELSE NULL END";
+
         // Build query with optional optimistic locking
         if ($expectedUpdatedAt !== null) {
             // Optimistic locking enabled - check that updated_at hasn't changed
@@ -227,7 +230,8 @@ class TicketModel {
                     category = ?,
                     type = ?,
                     updated_by = ?,
-                    updated_at = NOW()
+                    updated_at = NOW(),
+                    $closedAtClause
                     WHERE ticket_id = ? AND updated_at = ?";
         } else {
             // No optimistic locking
@@ -239,7 +243,8 @@ class TicketModel {
                     category = ?,
                     type = ?,
                     updated_by = ?,
-                    updated_at = NOW()
+                    updated_at = NOW(),
+                    $closedAtClause
                     WHERE ticket_id = ?";
         }
 
@@ -250,7 +255,7 @@ class TicketModel {
 
         if ($expectedUpdatedAt !== null) {
             $stmt->bind_param(
-                "sissssiis",
+                "sissssisis",
                 $ticketData['title'],
                 $ticketData['priority'],
                 $ticketData['status'],
@@ -258,12 +263,13 @@ class TicketModel {
                 $ticketData['category'],
                 $ticketData['type'],
                 $updatedBy,
+                $ticketData['status'],
                 $ticketData['ticket_id'],
                 $expectedUpdatedAt
             );
         } else {
             $stmt->bind_param(
-                "sissssii",
+                "sissssisi",
                 $ticketData['title'],
                 $ticketData['priority'],
                 $ticketData['status'],
@@ -271,6 +277,7 @@ class TicketModel {
                 $ticketData['category'],
                 $ticketData['type'],
                 $updatedBy,
+                $ticketData['status'],
                 $ticketData['ticket_id']
             );
         }