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>

handlers/messages.js

@@ -3,7 +3,7 @@
  */
 const { mongoose } = require('../db-connection');
 const { CONFIG } = require('../config');
-const { extractRawEmail } = require('../utils');
+const { extractRawEmail, isStaff } = require('../utils');
 const { getGmailClient, sendGmailReply } = require('../services/gmail');
 const { updateTicketActivity } = require('../services/tickets');
 const { getNotifyDm } = require('../services/staffSettings');
@@ -19,12 +19,11 @@ async function handleDiscordReply(m) {
   const ticket = await Ticket.findOne({ discordThreadId: m.channel.id }).lean();
   if (!ticket) return;
 
-  // Track whether last message is from staff or customer
   const memberForCheck = await m.guild.members.fetch(m.author.id).catch(() => null);
-  const isStaffMember = memberForCheck && CONFIG.ROLE_ID_TO_PING && memberForCheck.roles.cache.has(CONFIG.ROLE_ID_TO_PING);
+  const isStaffMember = isStaff(memberForCheck);
   Ticket.updateOne(
     { discordThreadId: m.channel.id },
-    { $set: { lastMessageAuthorIsStaff: !!isStaffMember, lastActivity: new Date() } }
+    { $set: { lastActivity: new Date() } }
   ).catch(() => {});
 
   // DM the claimer if they have notifydm on and a non-staff user replied.