simplify: prune dead code, dedup gmail send, drop neutered log stubs

- Remove no-op log stubs (logGmail, logAutomation, logSecurity, logSystem)
  and ~17 callsites; dead counters in tickets.js and gmail-poll.js go too
- Dedup three near-identical Gmail send paths into sendThreadedEmail helper
- Drop dead Mongoose fields: broccoliniTicketId, lastSyncedBroccoliniArticleId,
  renameCount, renameWindowStart, reminderSent, staffChannelId,
  unclaimedRemindersSent, lastMessageAuthorIsStaff
- Drop dead config fields and their .env.example entries
- Inline api/botClient.js (3-line wrapper, 2 callers)
- Trim unused exports across utils.js, tickets.js, configSchema.js, debugLog.js
- Fix handlers/messages.js to use isStaff() — old partial check ignored
  ADDITIONAL_STAFF_ROLES, so those members were treated as customers
- Drop unused deps p-queue + dotenv-expand; move mongodb to devDependencies

Net: -583 LOC source + -57 LOC lockfile. All 23 modules load clean.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

package.json

@@ -2,13 +2,13 @@
   "dependencies": {
     "discord.js": "^14.25.1",
     "dotenv": "^17.2.4",
-    "dotenv-expand": "^11.0.6",
     "express": "^5.2.1",
     "express-rate-limit": "^8.3.2",
     "googleapis": "^171.4.0",
-    "mongodb": "^7.1.0",
-    "mongoose": "^6.12.0",
-    "p-queue": "^6.6.2"
+    "mongoose": "^6.12.0"
+  },
+  "devDependencies": {
+    "mongodb": "^7.1.0"
   },
   "name": "broccolini-bot",
   "version": "1.0.0",