Add per-staff metrics: StaffAction event log + /stats command

Event-sourced tracking of staff/ticket lifecycle actions, plus a /stats
command. Foundation for a future tickets-website analytics dashboard.

Data:
- StaffAction model (event log) + Ticket.game / Ticket.closedAt
- STATS_ADMIN_IDS config (who may view others' stats)

Recording (fire-and-forget, idempotent on real state transitions):
- claim, response (channel reply + /response send), escalate, de-escalate,
  transfer, close (4 sites), reopen — each denormalizes ticketType, tier,
  priority, game, requester (senderEmail / creatorId), guildId
- close events carry closerType / resolverId (claimer credit) / wasClaimed;
  transfer carries fromId / toId; reopen stamps resolverId
- conditional close transition helper (atomic open->closed + closedAt) shared
  by all four close paths

Query + command:
- pure period parser (presets + free-text) and stats shaper (per-metric keys)
- command-aware autocomplete dispatch
- /stats: period (autocomplete) + member (admin-gated) + source (all/email/
  discord), ManageMessages + staff-role gated, ephemeral, tier-labeled embed

288+ unit tests; timing/busiest-times data is collected but displayed later.

gmail-poll.js

@@ -26,6 +26,7 @@ const { getNextTicketNumber, checkTicketLimits, getOrCreateTicketCategory, toDis
 const { logError } = require('./services/debugLog');
 const { enqueueSend } = require('./services/channelQueue');
 const { getTicketActionRow } = require('./utils/ticketComponents');
+const { recordAction } = require('./services/staffStats');
 
 const Ticket = mongoose.model('Ticket');
 const Transcript = mongoose.model('Transcript');
@@ -250,6 +251,54 @@ function oauthSuspendIfPermanent(err, client) {
   return true;
 }
 
+// ============================================================
+// Email ticket persistence (Part A: game; Part B: reopen recording)
+// ============================================================
+
+/**
+ * Upsert the email ticket record and, when wasReopened is true, fire-and-forget
+ * a 'reopen' StaffAction with resolverId = the prior claimerId from the
+ * returned doc (claimerId is never cleared by any close path).
+ *
+ * Injectables: _Ticket (Ticket model), _recordAction (staffStats.recordAction).
+ * Exported for unit testing.
+ */
+async function persistEmailTicket(fields, guildId, wasReopened, _Ticket, _recordAction) {
+  const {
+    threadId, discordThreadId, senderEmail, subject, createdAt,
+    ticketNumber, priority, parentCategoryId, game
+  } = fields;
+
+  const doc = await withRetry(() => _Ticket.findOneAndUpdate(
+    { gmailThreadId: threadId },
+    {
+      $set: {
+        discordThreadId,
+        senderEmail,
+        subject,
+        createdAt,
+        status: 'open',
+        ticketNumber,
+        priority,
+        lastActivity: createdAt,
+        parentCategoryId,
+        game
+      }
+    },
+    { upsert: true, new: true }
+  ));
+
+  if (wasReopened && doc) {
+    _recordAction('system', 'reopen', {
+      ticket: doc,
+      guildId,
+      resolverId: doc.claimerId ?? null
+    });
+  }
+
+  return doc;
+}
+
 // ============================================================
 // Orchestrator
 // ============================================================
@@ -287,6 +336,7 @@ async function poll(client) {
           .select('gmailThreadId discordThreadId status')
           .lean();
 
+        const wasClosedTicket = !!existing && existing.status === 'closed';
         let ticketChan = null;
         let parentCategoryIdForTicket = null;
         let isReopened = false;
@@ -368,23 +418,23 @@ async function poll(client) {
 
           const now = new Date();
           const defaultPriority = CONFIG.PRIORITY_ENABLED ? CONFIG.DEFAULT_PRIORITY : 'normal';
-          await withRetry(() => Ticket.findOneAndUpdate(
-            { gmailThreadId: parsed.threadId },
+          await persistEmailTicket(
             {
-              $set: {
-                discordThreadId: ticketChan.id,
-                senderEmail: parsed.senderEmail,
-                subject: parsed.subject,
-                createdAt: now,
-                status: 'open',
-                ticketNumber: number,
-                priority: defaultPriority,
-                lastActivity: now,
-                parentCategoryId: parentCategoryIdForTicket
-              }
+              threadId: parsed.threadId,
+              discordThreadId: ticketChan.id,
+              senderEmail: parsed.senderEmail,
+              subject: parsed.subject,
+              createdAt: now,
+              ticketNumber: number,
+              priority: defaultPriority,
+              parentCategoryId: parentCategoryIdForTicket,
+              game: detectedGame
             },
-            { upsert: true, new: true }
-          ));
+            guild.id,
+            wasClosedTicket,
+            Ticket,
+            recordAction
+          );
 
           // New (or reopened) ticket: file the email thread into Triage — out of
           // the inbox, marked read, awaiting staff action. The threads.modify also
@@ -404,4 +454,4 @@ async function poll(client) {
   }
 }
 
-module.exports = { poll, setPollSuspended };
+module.exports = { poll, setPollSuspended, persistEmailTicket };